Let f(x)=," 1 Use the definition (first principle) to determine the 1-x derivative of ƒ(x).

Q: Compute the derivative of g(x)=arctan(x^3+1)

A: From the given data:

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: 1/x using the definition o

A: we have to find the derivative of f(x) using the first principal. f(x)=x+1x

Q: Use Leibniz’s Rule to find the derivatives of the functions

A:

Q: 1 Use the power rule to find the derivative of f(x) = Vx 15 f'(x) = %3D

A:

Q: Find the derivative of 1 f(x) || 1+ Vx using the definition of derivative. State the domain of the…

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

Q: Show both the Newton and Leibniz notation for finding the derivative of y = f(x) = 4x5.

A:

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: Define the derivative of f(x) at x =a

A: For a function f(x), the derivative is defined as: Now at x=a, the derivative is defined as:

Q: Find the derivative of the function at the given number. f(x) = 3 – 4x + x², at -1 %3D f'(-1) = %3D

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: find the derivative of the transcendental function y=e^x-cotx

A: Given,             y=ex-cotx

Q: Define the second derivative of f. If f(t) is the position  function of a particle, how can you…

A: Second derivative is derivative of the derivative.      Therefore,…

Q: Apply the second derivative test to find all relative extrema. (c) f(x) = 1

A: To find the relative extrema first we  find the critical points. The critical points are the values…

Q: Find the derivative of f(x) at the designated value of x (Using Derivative Rules). 3 11. f(x) = x*,…

A:

Q: State the theorem for Second Derivative Test for f (x, y).

A: The second-derivative test for maxima, minima, and saddle points has two steps. 1. Find the critical…

Q: 3. Calculate the derivative of f (x) = x2 +1 showing all your work.

A: Using the formula u by v = vd/DX(u)-u d/DX(v)/v^2 According to the bartleby guidelines I can  solve…

Q: 8. Find the derivative of f(x) = (1+x³)' ( 14x + - ) using differentiation rules.

A: topic - derivative of a function

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

A:

Q: 2. Use the definition of the derivative to find f'(x) and f"(x). a) f(x) = x? %3D

A:

Q: Find the derivative using the definition of the derivative for f(x) = Vx (ie. f'(x) = fn &+h)-{(x) ,…

A:

Q: 7 Let f(x) x – 9 * Then according to the definition of derivative

A:

Q: Consider the function as folows:-   r(x) = 2x - 5 /(3x + 1)2 In general, how do you find the…

A: Given function: rx=2x-53x+12 We can write the function as rx=2x-53x+1-2 Differentiate the above…

Q: Use the second derivative to find the location of all local extrema for f (x) = x + x2 – x3, -

A:

Q: A) Consider the function f(x) whose second derivative is f"(x)=4x+3sin(x). If f(0)=4 and f'(0)=4,…

A:

Q: f(x) = tan (5æ).

A:

Q: Is the function f(x) = |x| cos x differentiable at the point x = 0 ? (Use definition of the…

A: if lim∆x→0f(∆x+x)-f(x)∆x doesn't exist then not differential

Q: Find the derivative of the function using the definition of derivative. f(x) = x4 f'(x) = %3D

A: To find the derivative of the given function using the definition of derivative.

Q: 2. Find the derivative of f(x). (a) f(x) = x² sec x (b) f(x) = 1+ tan a 1- tanz

A:

Q: What is the derivative of f(x)=−cos(x)+4sin(x) at the point x=−π/2?

A: We will find the derivative as following.

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: Prove, using the definition of derivative, that if f(x) = cos x then f ' (x) = - sin x

A: we have to prove by using the definition of derivative that if f(x)=cosx then f'(x)=-sinx   as we…

Q: Estimate the derivative of the function f (x) = -3 at the point a = 3. %3D

A: Here given as fx=x3-3 Differentiate with respect to x f'x=ddxx3-3=ddxx3-ddx3=13

Q: Find the derivative of the transcendental function. f(x) = x2 tan(x) f'(x)

A: As we know we if a function is multiplication of two or more than two functions it's derivative is…

Q: 1. Use the limit definition of the derivative to determine the derivative.2. Determine the equation…

A: We have to find derivative using limit definition of derivative and then find tangent line to f(x)…

Q: Shows that if a function f(x) is continuous in interval [a,b] then most likely the derivative of…

A:

Q: Find the derivative of the function using chain rule. f(x) = esin?x

A:

Q: Find the derivative of the function f(x) v4-x by definition

A:

Q: Find the derivative of the function. f(x) 4. + 2cos x %3D

A:

Q: Find the derivative of f(x)=x2-3x. Use the result to find the slope of the tangent line to the curve…

A: Given: fx=x2-3x To Find: The derivative of the given function and the slope of the tangent line at…

Q: 2х Use the Limit to determine the derivative of f (x) Then X-1 check your result by using the…

A:

Q: Compute the derivative of the function f (x) = tan x2 +1

A:

Q: Find the derivative of the function using the definition of derivative. 1 f(x) V5 + x

A:

Q: What is the derivative of f(x) sec(tanx)?

A:

Q: 14. Find the derivative of the function using the definition of derivative. f (x) = V1 – x

A: Derivatives

Q: Find the derivative of the function. f(x) = tan(5x²) %3D f'(x) = %3D

A: To find the derivative .

Q: Find the derivative of the function f(x) = v4-x2 by definition

A: The given function is f(x)=4-x2 The definition of the derivative is given by: If a function f(x) is…

Q: B) Use the definition of differentiation to find the derivative of the function f(x) = 4- Vx + 3. Is…

A: Consider the function: fx=4-x+3 The definition of derivatives is given by the formulas,