Use the definition of derivative to compute f '(0). e-1/x if x * 0 if x - 0 f(x) f '(0) -

Q: If ƒ(x) = x^n, n>=1, show from the definition of the derivative that ƒ′(0) = 0.

A: Given,

Q: Find the derivative of f(x) = sin x²+ cos x if f'(2)

A: Given function is fx=sinx2+cosx. It is differentiated as follows by using the sum rule of…

Q: Find the derivative of the function.

A: Given: To find: Derivative

Q: Find the derivative of the function f(x) = (In x)°.

A: Given that,             f(x) = lnx3 Differentiating with respect to x, we get                  f'(x)…

Q: Compute the derivative f'(x) for f(x) = log(x*) sin(x³).

A: Topic - derivative

Q: Find the derivative of the function.

A: Given function is By using the properties of logarithm, ln(a/b)=ln(a)-ln(b) and ln(a^b)=bln(a), we…

Q: Compute dy/dx using the limit definition of the first derivative for f(x) = 3x2

A: Given function is f(x)=3x2. we have to find the derivative using limit definition .

Q: Prove, using the definition of derivative, that if f(x)  = Cps x,then f'(x) =- Sin x

A: Given fx=cos xBy definition of derivativef'x=limh→0 fx+h-fxhfx=cos xThereforef'x=limh→0 cosx+h-cos…

Q: HiHtar is THe secoyd derivative OF Y

A:

Q: find the derivative of f (x) at the designated value of x. f (x) = 1x at x = 1/16

A: Given: fx=1x To find the derivative  Differentiate the given function with respect to x we get,…

Q: f(x) = cos (x – a -2).

A:

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: Find fifth order derivative of the function f(x) = x*Sin (2x +1) by using Leibnitz theorem.

A:

Q: Find the derivative of f(x) with respect to x ( f(x) = cos(x), find the f(x) by using the…

A: Given;  f(x)=cosx.

Q: Find the derivative of f(x) = Inx + 1].

A: f(x) = ln [x2x2+1]f'(x) = ddx[ ln [x2x2+1] ]f'(x)= 1 x2x2+1 ddx[x2x2+1]

Q: Determine the derivative of f(x) = ( In x )6 with respect to x. f'(x) =

A:

Q: 2. Find the first derivative given that f(x)=x√√x + 1 x²√x

A:

Q: Find the derivative of function.

A:

Q: find the derivative of f (x) at the designated value of x. f (x) = x3 at x = 12

A: The derivative of a function can be calculated by differentiating both sides of the function with…

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.

A:

Q: find the derivative of y with respect to the appropriatevariable. y = cos-1 (x2)

A: Given function is y=cos-1x2. Chain rule of differentiation states that: ddxfgx=f'gx·g'x…

Q: Find the derivative of the function. 3x2 g(x) • dt 4 + t3 tan x g'(x) =

A:

Q: Compute the second derivative of sin(g(x)) at x = 2, assuming that g(2) = π/4 , g'(2) = 5, and g"(2)…

A: singx

Q: find the derivative of y with respect to the appropriatevariable. = cosh-1 2√x + 1

A: Given: y=cosh-12x+1Here ,we havecoshy=2x+1Taking the derivatives on both…

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: 3x g(x)=e* In(4x+1) (с)

A:

Q: Find the derivative of the function. • 2x2 g(x) = 1 dt 3 + t3 /tan x g'(x) =

A:

Q: Find the derivative of the function by the limit process. f(x) = 1/x2

A: Here the given function The first derivative of function f(x) is defined by limit prosses as

Q: find the derivative of f (x) at the designated value of x. f (x) = x5 at x = 3/2

A: Given function is: fx=x5 We have to find the derivative of f(x) at x=32. Then we get,…

Q: Let f (x) = 7 cos(Tx). Find the twentieth derivative of f (x).

A:

Q: Find the weak derivative of f() = |x² – x + 1/5| on the 1) interval (0,1).

A:

Q: Which of the following has a derivative of f (x) = 2x (arctanx + arccotx)?

A:

Q: Find the derivative of Vry = -3+x*y° using implicit differentiation.

A:

Q: Give the derivative of f(x) arctan an(e³*) at the point where x = 0.

A:

Q: Find the derivative of flx) = x 1x \ - Does plo) exist

A:

Q: Find the derivative of the function by the limit process. f(x) = vX +7

A: Given,          The function is fx=x+7.

Q: Find the derivative of f(x) = e" – a3 +In(x) - In(x)

A:

Q: Compute the second derivative of sin(g(x)) at x = 2, assuming that g(2) = 4, 8'(2) = 5, and g"(2) =…

A: Given: The function singx with g2=π4, g'2=5, and g''2=3, To find: The second derivative of given…

Q: 1 m' (x) = x In(x)

A: Given: m'x=1xlnx for finding anti-derivative of given expression, we substitute lnx=u…

Q: Use backward, forward, and centered difference approximation to estimate the second derivative of…

A:

Q: Use a quick approximation to estimate the derivative of the given function at the indicated point.…

A: f (x) = 1 − 2x  point,  x = 2 To use quick approximation to estimate the derivative, f'(2).

Q: Find the equation of the tangent line to the function f(x) = x² – 2 at the point (1,-1). You must e…

A: Given, fx = x4 -2  We have to find the equation of the tangent line to function at the point 1, -1.

Q: f(x) = x*Inx

A: TO FIND 5th order derivative f(x) = x4 lnx FORMULA USED  BIPART PRODUCT RULE OF DIFFERENTIATION…

Q: If ƒ(x) = xn, n ≥ 1, show from the definition of the derivative that ƒ'(0) = 0.

A: Now the derivative of a function f at a point 'a' is given by,

Q: What is the derivative of the function B(x)=3/(x+2) at x=a?

A:

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

A:

Q: By using first principle, show that the derivative of f(x)=- is x+1 1 S'(x) = (x+1)

A:

Q: Find the derivative off with respect to x of f(x) = In x⁹. The derivative off with respect to x of…

A:

Q: 2 Use the definition of derivative to find the equation of line tangent to f(x) = 2 through x = 3.

A: