b) Find the equation of the line tangent to the graph of y=log; (5x +1) at x = 2

Q: nd the equation of the tangent line to the graph of ƒ(x) = (1+x³)−² at the point

A: Topic:- application of derivatives

Q: A curve is given by the equation y = ln (2³+¹). x5

A:

Q: Find an equation of the tangent line to the graph of the function at the given point

A: To find the slope we find y' at x=0, y=0

Q: In the given equation as follows, find an equation of the tangent line to the graph of the function…

A: Given: y = log3x and the point (27, 3). To find: The equation of tangent line at the given point.

Q: find an equation of the tangent line at the point indicated. R(z) = log5(2z2 + 7), z = 3

A:

Q: Find the equation of the line that is tangent to the graph of the function f(x) = ln(8x + 6) at the…

A:

Q: Find the equation of the tangent line to the graph of f(x) = In x at xo = e 8.

A:

Q: Find the equations of the tangent lines to the graph of y = ln  x  at x = 1 and x = -1.

A: To find equation of tangent lines at x=1 and x=-1f(x)=lnx

Q: Without using a graphing calculator, how can I show the function 1-ln(y )= z in a graph and its…

A: Without using a graphing calculator,  Show the function zx,y=1-lny in the graph and its traces.

Q: Find the equation of the line tangent to the graph of y=log, (5x + 1) at x= 2

A:

Q: Find an equation of the tangent line to the graph of the function at the given point. y = ln(x7/2);…

A:

Q: #36 Find the equation of the tangent line to the graph of X²(x²+y²) = y? at

A:

Q: Find the equation of the secant line for f(x) = log2 (3x² + 2x – 1) from x = 1 to x = 3.

A:

Q: Find the derivative of the function f(x)=ln(10e^13x−7).

A: Note: Since you didn't use parenthesis while writing the function, there can be two possibilities…

Q: At what point on the curve y = [ ln (x +4 ) ]2

A: Consider the curves, y=lnx+42

Q: Find the derivative of the given log(cot(1-x2))

A:

Q: Find an equation of the tangent line to the graph of Y = e2x-3 at the point (3/2,1).

A:

Q: Find an equation of the tangent line to the graph of the function  y = log3 x, at the given point…

A: y = log3 x

Q: Find an equation of the tangent line to the graph of the function y = log10 2x, at the given point…

A: Given:y=log10 2x  through the given point 5, 1Equation of tangent line:y-y1=mx-x1Slope:dydx=f'x=m

Q: y = √√2x + 7

A:

Q: 5. Find an equation of the tangent line to the graph of f(x) = In (2x + 1) – e* at the point where x…

A:

Q: Determine the equation of the tangent line to the graph of y = f'(x) at the point where x = 1 if…

A:

Q: Calculate the derivative of the following function. y = log 11(x-11) d. dx log 11(x- 11) =

A:

Q: 25.For which x – values does the graph of y = e3x³-2x-4x have a horizontal tangent line ?

A:

Q: How to solve the derivative of this

A:

Q: Find the second derivative (y") of y = cot(3x³)

A: Given,        y=cot(3x3)

Q: Find an equation of the tangent line to the graph of y=e^-x^2 at the point (2,1/e^4)

A:

Q: 7. Determine the equation of the tangent to the function E-2 f(x)=- at x= 1.

A:

Q: Find an equation of the tangent line to the graph of y = e−x2 at the point 4, 1/e^16

A: Given curve

Q: Find the indicated derivative and simplify. log 5x y' for y = 4+x5

A: Given   y = log5x4+x5we need to find y'

Q: Find the equation of the line tangent to the graph of y = (x2 - x) ln (8x) at x = 2

A: Topic = Derivative

Q: Find the equation of the tangent line at the given point on each curve. ln(x + y) = x3y2 + ln (x2 +…

A: The equation of the tangent line at the given point (x1,y1) is y=mx+b where m is slope m=dydxx1,y1…

Q: Find an equation of the tangent line to the graph of the function at the given point. g(x) = ex3 −…

A: We have been given a function g(x) and we need to find the equation of tangent line to the graph of…

Q: Find the equation of the tangent line to the graph of function at the given point. Y = 5+ 1n(1-4x) ;…

A:

Q: Find the equation of the tangent line to the graph of f(x) at x = 2, if 25 f(x) = 2.5 + log5 2 (x -…

A: For x=2 f(x)=2·5x+log5252xf(2)=2·52+log5252(2)f(2)=2(25)+log525f(2)=50+2f(2)=52 So the point is…

Q: Find the equation of the tangent line to the curve at point (0, ln 2).   y=ln(e^x+e^4x)

A: the equation of the given curve is: y=lnex+e4x we have to find the equation of the tangent line to…

Q: Find an equation of the tangent line to the graph of y=e^-8x at the point (5,e^-40)

A: To find an equation of the tangent line to the graph of y=e-8x at the point (5,e-40).

Q: 2. Find the equation of the tangent line to the graph of f(x) = 3x?e-1 - 1, at r = 1.

A:

Q: Find an equation of the tangent line to the curve at the point (1, 1/e)   y = x3e−x

A: Given query is to find the equation of tangent line to the curve   y = x3e-x

Q: Find an equation of the tangent line to the graph of the function at the given point.   f(x) =…

A: Given,     f(x) = ln(9(x+4)/x); (-9/2,0) Let m be the slope of required tangent line.

Q: Find the equation of the tangent line to the function f (x) = e*²-1 ln(x + 1) when x= 0.

A:

Q: Find an equation of the tangent line to the graph of the function at the given point, y = e3x−x2,…

A: Given equation: y=e3x-x2 The equation of the tangent passing through the point x1,y1 on the curve…

Q: y = e2x+1

A:

Q: Find an equation of the tangent line to the graph of  y = e−x2  at the point (5, 1/e power of 25)

A:

Q: Find the derivative of the exponential function f ( x ) = 5x 2 e 7x

A: Given function: f(x)=5 x2 e7x     Calculate the derivative of f(x): f(x)=5 x2 e7x   Take the…

Q: Find the equation of the tangent line to the graph f (x) = x^3 ln x at the point (1, 0)

A: Tangent line equation.

Q: Find an equation of the tangent line to the graph of the function h(x) = −xe2−x, at the given point…

A: Slope of the tangent line is the derivative of the given curve at the given point. So…

Q: 1- Find the first derivative of y with respect to x for the following functions: In5 7x y = log5 . a…

A:

Q: Find an equation of the tangent line to the graph of (log æ)cosh(a-10) , x >1 at the point where x =…

A: Given equation is  y=log xcosh (x-10), x>1 at x=10

Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as: