Use the definition of a derivative to show that if f(x) = 1/x, then f'(x) = -1/x². (This proves the Power Rule for the case n = -1.) %3D

Q: Find the derivative of f(x) = COS 4 log3 (x²) os(5x)

A: Explanation of the answer is as follows

Q: What is the first derivative of s(x)=(7x)3x at x=4?

A: To evaluate s'(4)

Q: Find the 7th derivative of: f(x)=sin(x)cos(x) f’=? • • •

A:

Q: Use three-point midpoint formula to evaluate the first derivative of y = cos(x) at x = 5 using a…

A: Given function is y=cosx. We have to find the first derivative of y=cosx at x=π2 using a value of…

Q: Find the derivative of f(x) = 3x° cos(x). 8 CoS f'(x)

A: Given query is to find the derivative of the function.

Q: By using the definition of the derivative, find the for: - dx 1- f(x) = Vx

A:

Q: How to solve for the derivative of Dy[tan(y)+1/tan(y)-1]? If it's 0, why?

A:

Q: Find the derivative of function.

A: The given function is f(x) = ln(xex+2).We have to find the derivative of this function with respect…

Q: HiHtar is THe secoyd derivative OF Y

A:

Q: Compute the derivative of f(x) = 7 ln (x + 10) + In (x³ ): Answer: f'(x) =

A: Given function is  f(x)= 7ln(x+10) + ln(x3), we have to find the derivative of f(x) with respect to…

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: Use forward-difference formula to evaluate the first derivative of y = tan(x) at x = 1 using a value…

A: The two-point forward difference formula to calculate f'(x) is f'(x)=f(x+h)-f(x)h, where h is the…

Q: Use the First Derivative Test to find the relative extrema of ƒ(x)=· sin x on (0,27).

A: The given function is- fx=x2-sinx  Differentiating f(x) w.r.t x- f'x=12-cosx Put f'x=0,…

Q: 13. f(x) = e* In x

A:

Q: Find the second derivative of function, and then find ƒ″ (1)  and ƒ″ (−3) .

A: Find first the derivative as shown below: f'x=ddx-5-x2        =125-x2ddx5-x2       =-125-x2-2x…

Q: 2.) Compute for the derivative (DO NOT USE THE DEFINITION) of A. 2x3 y = tanh sin x2

A:

Q: Find the 46th derivative of y = cos (x) sin (a) cos (2) cos (x) - - sin (x)

A: Given y=cosx

Q: Use forward-difference formula to evaluate the first derivative of y = sin(x) at x = O 2√2 π -2√2 ㅠ…

A: Given that y=sinx. We have to find the first derivative of y=sinx at x=π2 using a value of h=π4 by…

Q: Evaluate the derivative of y = sin'6x + In /1- 36x, where x= 0.125. dx |x= 0.125 U (Type an integer…

A:

Q: Find the 139th derivative of y=cos x а. Cos x b. Sin x С. -Cos x d. -Sin x

A:

Q: Compute the derivative using derivative rules. y= cos(1/x) / (1 +x 2)

A: Derivative: The rate of change of a function with respect to a variable. y=fxy'=limh→∞ f(x+h)-f(x)h

Q: Find the derivative of ,In sin-1) y = e %3D

A:

Q: Find the derivative of the function f(x) = 5ª+x² + log3 (In x). %3D

A: To find the derivative of the given function.

Q: fcx)= Y文 メ ー^

A: Local extrema

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

A: fx=sinx2+cosx

Q: Find the second derivative of f(x) = sin(3x) - cos(2x)

A: We have to find second derivative of  f(x) = sin(3x) - cos(2x)  Then   First derivative of f(x) is…

Q: Find the anti-derivative of: f(3x^3+9x)^6 (x^2+1)dx

A:

Q: FInd the derivative of f(x) =ln 1+ex/1-ex

A:

Q: what the derivative fxy er hin ction Sas)=x'tan)

A:

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

A:

Q: Find the derivative of f(x) = 9 sinh-' (x²) – 9 In ( Vx4 + 1). %3D

A:

Q: Find the derivative of the function g(x) = (arctan x)³, first showing how to get the formula for -…

A: Consider the function  g(x)=tan−1x3

Q: Use forward-difference formula to evaluate the first derivative of y = cos(x) at x = using a value…

A: Given we have given the function y=cos(x) we have to find the first derivative of y = cos(x) at x =…

Q: Find the derivative of the following using the three-step rule 2. y=Va² +x

A:

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

A:

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: Find the derivative. 8 + e y = In 8 + et 8 - ex.

A: Given,          y=ln8+ex8-ex

Q: Use forward-difference formula to evaluate the first derivative of y = tan(x) at x = 4 using a value…

A: Given function is y=tanx. We have to find the first derivative of y=tanx at x=π4 using a value of…

Q: Compute forward difference approximations for the first derivative of the function, y = cos(sin(x)+…

A: Given is the function  y=cos(sin(x))+1) Forward difference is found as:F'xi=Fxi+1-FxiΔx

Q: Find the derivative of f ( x ) = 6 sin ^2 ⁡( x ) + 6 cos^2 ⁡( x ) at x = -6.5

A:

Q: 1 erivative of x²+2

A:

Q: Use forward-difference formula to evaluate the first derivative of y = sin(x) at x = using a value…

A: Given function is y=sinx. We have to evaluate the first derivative of y=sinx at x=π2 using a value…

Q: Find the first derivative of the function below: f(x) = arctan(sec(x ))

A:

Q: find the derivative of the fuction f(x)= 5sinx/3x+cosx

A:

Q: Show that the derivative of f(x) =xln(x)−x is ln(x). Use this to compute∫ln(x)dx.

A: Sum/difference rule of differentiation,

Q: Obtain the first derivative of the function f (x) = sinx/x using Richardson's extrapolation with h =…

A: Given  f(x) = sinxx we have to obtained the first derivative of f(x) by using  Richardson's…

Q: Use three-point midpoint formula to evaluate the first derivative of y = sin(x) at x = using a value…

A: To find- Use three-point midpoint formula to evaluate the first derivative of y = sinx at x = π2…

Q: Find the derivative to by implicit differentiation Sinx +4 cos y=3

A: