Calculate the derivative of the function y=(x−1)(x−2)2 without using the product rule for the derivative.

Q: Find the derivative of y = x3 – 6x², using first principle.

A:

Q: Find the derivative of the function  y = ln (8x3-x2)

A:

Q: Find the derivative of the function using Chain Rule. h(x) = (2x-6)-¹ (x²+3)

A:

Q: Find the 3rd derivative of the function y=f(x) given by the equation y2=2x.

A: First we solve the given expression for y

Q: Find the nth-order derivative of the function y=x3sin2x.

A:

Q: Find the derivative of the function. f(x) = ex In(x³) f'(x) = X

A:

Q: Find the derivative of the function f(x) = ln(3x2 + 2x)

A:

Q: Find the derivative of the function. + 2 (x) = ex2. f'(x) %3D

A:

Q: Find the derivative of y=3x^x

A: Given,

Q: find the derivative of y = x3/x

A: Given y=x3x

Q: Find the derivative of the function. h(x) = ex² - > x + 5 %3D

A:

Q: Find the derivative of the function using the definition of derivative. 1 g(x) 8 + Vx g'(x) =

A:

Q: Find the derivative of the function:  f(x)=x^2lnx

A: consider the given function:

Q: Find the derivative of y = ÷+; x2

A:

Q: Find the derivative of the function y=x2+3x+1x without using the quotient rule for the derivative.

A: Given: y=x2+3x+x we know that ddxxn=nxn-1

Q: Determine the second derivative of the implicit function  x2+2xy+3y2=2

A: Product rule of differentiation: ddxf(x)g(x)=f(x)ddxg(x)+g(x)ddxf(x) Power rule of differentiation:…

Q: Find the derivative of the function y=2√x−3sinx.

A: Given: fx=2x-3sinx for finding derivative of given function we use property given below…

Q: Find the derivative of [(xt1)*] /x.

A:

Q: Find the derivative of function.

A: We have given y=-2ln x3x-1. Differentiate both sides with respect to x. Use constant multiple rule…

Q: Find the derivative of f (x) = 1x , x = 0.

A: Given: f(x)=x at x=0

Q: Calculate the derivative of the function y=2√x+33√x.

A: Given function is y=2x+33x Power rule of differentiation states that: ddxxn=nxn-1 Differentiating…

Q: Find the derivative of y = x2".

A: Find the derivative

Q: Find the derivative of the function f(x)=x-2/2+x square root

A:

Q: Use implicit differentiation to find the 2nd derivative of x2 y + y2 x=-2

A: By using implicit differentiation to find the 2nd derivative of x2y+y2x=-2.

Q: Compute the derivative using derivative rules  y = (x2 + 9x)- 2

A:

Q: y=x²

A: I have stated the used formula in the solution

Q: Find the derivative of the function g(x)=x3∫x2tdt.

A:

Q: find the derivative of y if X(メ+リ(メ-2) (x)くメ+3)

A:

Q: Find the derivative of the function f(x)= xsinx+x^2e^2-1.

A:

Q: Find the derivative of the function. y = x2 In x2

A:

Q: Calculate the derivative of the function given by the equation x3+y3=3xy.

A:

Q: Calculate the derivative of the function y=(2−x3)(13+x2).

A:

Q: Find the derivative of y=x²sin⁴x+xcos²x

A:

Q: Calculate the derivative of the function y=x(2+3x) without using the product rule.

A: Given function is y=x2+3x. Given function can be written as y=2x+3x2. Power rule of differentiation…

Q: Find the derivative of the function. y= 2^(3-x^2)

A: Given function

Q: Find the derivative of y=x^3lnx

A:

Q: Find the derivative of the function.

A:

Q: Find the derivative of the function. y = x2V 49 - x2 y' =

A: Soove for differentiate

Q: Find the derivative of the function. g(x) = ex5 - 2x g'(x) = %3D

A:

Q: Find the derivative of f(x) = ln v4 – x2 %3D

A:

Q: Calculate the derivative of the function y=x2−x−1x without using the quotient rule.

A:

Q: Find the derivative of the function   f(x)=ln(x3(2x+1)/x^2−3)

A:

Q: Find the derivative of the function. f(x) = 2x In 2x %3D

A: Given, f(x)=2xln2x To find the derivative of f(x).

Q: Find the derivative of the function. y- 27-a

A:

Q: Find the derivative of the function. 12 X %3D

A:

Q: Find the derivative of the inverse function for y=x3−3x and calculate its value at x=−2.

A:

Q: w(x) %3D хе*

A: To find the second derivative of function w(x)=xex

Q: Calculate the derivative of the cubic function y=x3.

A: ddxxn=n xn-1

Q: Sketch the graph of y= x2+2/x by using the properties of the derivative.

A: Given: y=x2+2x=x2+2x⇒y'=1-2x2⇒x2-2=0 ;  ⇒x=±2 are…