Find the unit direction vector of greatest decrease of f at xo = [0 - 1 1]' and evaluate the derivative of the function at this direction.

Q: Find derivative of the function f(z) = (sin¬' (2z – 1))² with respect to z.

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Q: Find the derivative of the function by using the rules of differentiation. 4 f(u) = %3D f'(u) =

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Q: Compute the derivative of the function F (x) = L evi dt.

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Q: Find the derivative of f(y) = 2 sin y + sin² y and then use it to find all coordinates on the graph…

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Q: Find the gradient of the tangent line to y when x = 2.

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Q: Calculate the derivative using implicit differentiation: ∂w/∂z,x^3w+w^7+wz^2+2yz=0 ∂w/∂z = ?

A: To find the implicit derivative of the given equation.

Q: Find the derivative of the function.

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Q: Evaluate the derivative at x = 1 for y = In ()

A: For a function f its derivative is defined as f'(x)=limh→0f(x+h)-f(x)h. For some standard functions…

Q: (x-y) atfy (1, 1) a+y

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Q: Find the derivative of the function. F(x) = et dt

A: The function is given as F(x)=∫xx2et4 dt. The Leibnitz rule of differentiation under the integral…

Q: Find the derivative of the follourng funchion y=x sin'x %3D

A: We have to find the derivative of the given function   The given function is y=x sin-1x3it can…

Q: Use the definition of derivative to find the derivative of R(z) %3D

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Q: Find the equation of the tangent line to f(x) =1 – x² at (1,0). -

A: here we use formula  y-y1=m(x-x1) at point (1,0)

Q: Find the equation of the tangent line for f (x) = 2 sec(z) at z = 6

A: To find out the equation of tangent line.

Q: Find the derivative of the funciton F(x) = ,5t dt. F'(x) =

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Q: Calculate the derivative.

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Q: What is the derivative of y = ekx? For what values of k does this rule apply?

A: Given function is, y=ekx. The derivative of the given function is found as follows: dydx=ddxekx=kekx

Q: Find the derivative of the function. 1 3x' g(x) = dt 1 + t4 Jtan x

A: Given : g(x) = ∫tanx3x211+t4dt

Q: Find the general anti-derivative of f(x) = + Vx on a continuous interval.

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Q: Find the derivative of f(x) = (sin a)" %3D

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Q: Use the gradient to find the directional derivative of the function at P in the direction of PQ.

A: As we know that: The expression for the directional derivative  in the direction of a→ is:…

Q: Find the equation of tangent line to the curve f(x) = 2 – dt 1+t at the point x = 1.

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Q: Approximate the derivative of y=x at x=1 by forming small changes.

A: SOLUTION:-

Q: Evaluate the derivative at x = 1 for y = I (

A: Derivatives can be defined as rate of change of function with respect to an independent variable. It…

Q: Find the derivative of the funciton F(x) = dt. F'(x) =

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Q: Find the derivative. F(t) = In(sinh(2t)) %3D F'(t) %3D

A: Find the derivative of the function

Q: Find the derivative of the function.

A: we have to find the derivative of the function F(x)=∫1x1+t4dt

Q: Find the derivative of the function. f(z) = V - VE f '(x) =

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Q: Find the total derivative of V with respect to X

A: As the differentiation is with respect to x, x becomes the variable. y and z becomes constants

Q: Calculate the derivative using implicit differentiation: ∂w/∂z,…

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Q: Calculate the derivative using implicit differentiation: ∂w/∂z, x^4w+w^3+wz^2+2yz=0 ∂w/∂z=

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Q: V 92) Inl Cosn

A: Derivative of hyperbolic function

Q: Compute the derivative of h(sinx) at x = π,/6 , assuming that h' (0.5) = 10.

A: We have to compute the derivative of function hsin x at x=π6, assuming that h'0.5=10. We know the…

Q: Find the gradient of the tangent to the curve y = at the point with x 1. x+1

A: giveny=x2x2+1differentiatey'=(x2+1)2x-x2.2x(x2+1)2=2x(x2+1)2

Q: Find the derivative of function.

A: Use the product rule to find the derivative for s. s=t2lntdsdt=ddtt2×lnt+t2×ddtlnt

Q: Find the gradient of the tangent line to y when x =- 1

A: The explanation of answer as follows

Q: Find the derivative of f (y) In(y)

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Q: b) Use the method of Differentiation from first principle to prove that the derivative of the square…

A: To prove  ddxx=12xLet  f(x)=x

Q: b) Use the method of Differentiation from first principle to prove that the derivative of the square…

A: Consider the provided information, ddxx=12x Prove that left hand side is equal to right hand side.…

Q: Find the derivative of f(y) = ee") eelos f'(y) =

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Q: Find the derivative using the long method 3 u = t2

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Q: (d) Compute the driectional derivative of f at (1,2) in the direc- tion u = (e) • point (1, 2)? What…

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Q: calculate derivative of respect to x こ %3D dx

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Q: Find the derivative of the function In t dt.

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Q: Find the derivative.

A: Given,

Q: Compute the second derivative with respect to r of 3x + 8 y = at x = 1.

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Q: Approximate the derivative of y=x² at x=1 by forming small changes

A: We have to find the derivative of the function y=x2 at x = 1 by forming the small changes.

Q: Find the derivative of the given function a. F(x) = dt 1+ b. g(x) = [ - dt sinx 1+1*

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Q: Calculate the derivative of the function g(x)=x∫√x(t2−t)dt at x=1.

A: using the fundamental theorem of calculus we find g'(x)

Q: Find the gradient of the tangent line to the curve x² + y =10 at x=1, where y > 0. %3D

A: