Compute the derivative for y= (e^-4x sin^2(x)) / (x^2 + 3x + 1)

Q: Compute the derivative of the function y=arcsin1√x at x=2.

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Q: find the derivative of tihe unction?

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Q: fla)=-sinx (): In, Cosx

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Q: On which derivative rule is integration by parts based?

A: Integration by parts is based on product rule of derivative. Mathematically, Product rule of…

Q: y3D(i+sinx)(I-sinl)!

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Q: find the derivative of y with respect to the givenindependent variable.

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Q: (x²+1)* V1-x y = In

A: Use the chan rule of derivative then simplify the result.

Q: ) y = In³ )) (tanh²(scc '(x²)

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Q: Show that the derivative of the function sinh -¹ x can also be obtained by letting y = sinh -¹ x and…

A: Soln:To find the derivative of sinh-1x

Q: Compute the derivative using derivative rules that have been introduced so far y = √(9 +x + sinx)

A: We have to compute derivative of the function: y=9+x+sin x We know the formula of derivatives,…

Q: The second derivative of function: Inesina will be Select one: O sina O -sinz

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Q: Find the derivatives of the functions in Exercis

A: Given function is: y=1x sin-5 x-x3 cos3 x We have to find dydx.

Q: 2. Use logarithmic differentiation to find first derivative of y = (sinx)*

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Q: Find anti-derivative if possible of: sqrt(tan(x))  dx

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Q: 6. y%= arcsin a Va2-x2

A: Given: 6. y=xa2-x2-arcsinxa

Q: Calculate the derivative of the function y=1+cosxsinx.

A: Given: y=1+cosxsinx we know that for finding derivative of given function we need to use product…

Q: Compute the derivative using derivative rules that have been introduced so far y = cos4 θ

A: This question is taken from the derivative in which we have to find the derivative of the given…

Q: Find the derivative ofƒ(x) = 1/x5in two different ways:using the Power Rule and using theQuotient…

A: given: f(x)=1x5 the differentiation of the function f(x)=1x5 by using the power rule is: the…

Q: Find the derivative of the function

A: Given:y=arctanx+x1+x2Differentiate formula:ddxarc tanx=11+x2ddxuv=vdudx-udvdxv2

Q: Compute the derivative using derivative rules that have been introduced so far y = ex-12

A: To differentiate y=ex-12, with respect to x, apply the exponential rule of differentiation,…

Q: what is the first derivative of arccos4x

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Q: 1 y = ┤㈑┤慈┤

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Q: q? sin-! メ

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Q: Calculate the derivative of y=arctan√ex at x=0.

A: We differentiate both sides with respect to x using the chain rule.

Q: Find derivative of y=xsin2x

A: We will need product rule. Assume, u=x and v=sin2x. Now, we have u=x ⇒u'=dudx=dxdx=1  and v=sin2x…

Q: Find the derivative of y given that y = In (sinh x) %3D

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Q: Find the derivative of fcx) = en (sinh Cx)) 5

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Q: calculate the derivative y = ecosh−1 x

A: Given The chain rule of derivative is given by: The derivative of the inverse hyperbolic function…

Q: Find the derivative of y given that y= x In x et

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Q: Find the derivative of y = etanx

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Q: Find the derivative of y = arctan(x) by using implicit differentiation on x = tan(y).

A: Consider the provided function y=arctan(x).

Q: Find the second derivative if y = sinh- (n + x') at x = 0

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Q: 2 Find the derivative of y = arctan(x´ + 3)

A: We have to find the derivative of the given function.

Q: Find the most general anti-derivative

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Q: y = Vx* X

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Q: Find the derivative of y = 21+arctan x

A: By using derivative formula

Q: Find the derivative of the function. using chain rule y = sin(sin(sin x))

A: Given: y=sinsinsinx

Q: Find the derivative of y= sin cos (tan ax)

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Q: What is the Derivative of: y = extan x

A: Given: y=ex tan x To Find: dydx=?

Q: find implicit derivative dy/dx of x2sin2(y)+2x2=y

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Q: What is the Derivative of yx

A: f(x) = yx

Q: Calculate the derivative of the function y=arccos x arctan x at x=0.

A: Differentiating with respect to x, we get

Q: What is the derivative of: 4 ln(sec y + tan y) − 2x − sin 2x = 1

A: Given: 4 lnsec y+tan y-2x-sin 2x=1 To Find: dydx=?

Q: 2. Calculate the derivative of y = arccos(e arcsin(x2)

A: Let u=arcacos(e^x) and v=arcsin(x^2), then y=u/v

Q: Compute the derivative of y= arctan(arcsin x)

A: To Determine:  Derivative of given function:

Q: y = cos /sin(tan Tx) %3D

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Q: Find the derivative of using first principle?

A: we have to find first derivative of y by using first princple

Q: 1.Find the derivative of y = - arcsin %3D V4-x2

A: Given:        y=x4-x2-arcsinx2 differentiating on both sides     dydx=ddxx4-x2-arcsinx2…

Q: Find the derivative of the function. Simplify wherepossible  x lnarctan x

A: Let f(x)=xlnarctanxDerivative formula:ddxlnx=1xddxtan-1x=11+x2arctanx=tan-1x

Q: calculate the derivative y = (sinh−1(x2))3

A: Given The chain rule of derivative is given by: The derivative of the inverse hyperbolic function…