_y = In (x³ + 1)"|

Q: Choose the rule that you would use to most efficiently find the derivative of the function. f(x) =…

A: Given f(x) = 8√x^3

Q: Find the derivative of the function. f (x) = cube root of ( 1+ tant )

A:

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

A:

Q: Find the derivative. Simplify where possible. hx) = (1 - cosh x) /( 1 + cosh x)

A:

Q: Use the Product Rule or the Quotient Rule to find the derivative of the function.

A: Product rule is [ f(x)* g(x) ]'= f'(x) g(x)+ f(x) g'(x)

Q: use the definition of derivative to find the equation of the tangent line to the graph of f(x) = x2…

A: To find the equation of tangent line at the given point.

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

A: Let, y = xSquaring on both sides, we get;y2 = xDifferentiating on both sides, we get;2ydydx = 1dydx…

Q: f(x) = Arctan csc² ( 3x

A: Some derivative formulae: ddxtan-1x=11+x2ddxcscx=-cscx cotx Chain rule of derivative:…

Q: (x²+1)* V1-x y = In

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

Q: find the derivative using the appropriate rule or combination of rules. y = (x3 + cos x)−4

A: Given that, y=(x3+cosx)-4

Q: What is the derivative of y = (inverse tangent(3x))^2 ?

A: We will differentiate the given function with respect to X and use chain rule while differentiating.

Q: Find the derivative of ¤(x) at x = /3/2 where rsin-'(x) $(x) = eº tan 0 do. x2

A:

Q: use the General Power Rule, Exponential Rule, or the Chain Rule to compute the derivative. y = ex−12

A: Given function is y=ex-12. To find the derivative of the given function. Solution: Chain rule of…

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: Find the derivative. Simplify where possible.  f(x)= ex cosh x

A: Given function is

Q: Find both the derivative and indefinite integral of ƒ(x) = 4 cosh 2x.

A: Here given as ƒ(x) = 4 cosh 2x. Thus

Q: Find the derivative of the function without using the Quotient Rule. y

A:

Q: 2 - x f(x) = 3 x + 1

A: given that f(x)=2-x3x+1we need to find the derivative of the functionuse the quotient rule that is…

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: Obtain the second derivative of the function f(x) = 6 In(8x) – 3z4 and state the value of this…

A:

Q: Find the derivative of f(x)=arctan(1/x) and simplify

A:

Q: Find the derivative of ƒ (x) = /9 – 2æ. To enter va, type sqrt(a). f' (x) =

A: The chain rule says that when the terms inside a function being differentiated does not correspond…

Q: Estimate the derivative of f(x) = sin x at x = π/6.

A: Given,       f(x) = sin x at x=π6

Q: F(x) 1+ xe

A:

Q: Determine the derivative of y=(x−1)4 without using the power rule.

A:

Q: Find the derivative of the function without using the Quotient Rule. y =

A:

Q: Use the quotient rule to find the derivative of the following.

A: Given y=4x-3x

Q: Estimate the derivative of f(x) = sinx atx = ~-

A: Consider the provided function, fx=sinx at x=π2 Find the derivative of the function. First, we…

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

A:

Q: Use the First Derivative Test to find the relative extrema of x – 3 f(x) ex

A: The given function is fx=x-3ex. We need to find the realtive extrema. Concept used:  Consider x=c is…

Q: Find a function that has x^6 as its derivative without using integral knowlegde.

A: In this question, we need to find a function that has x6 as its derivative.

Q: 1 y = ┤㈑┤慈┤

A:

Q: 10. y = Jx

A: We have to find derivative of - y=f(x)=1x using delta method. Delta method to find derivative is…

Q: Find the derivative using the appropriate rule or combination of rules. y = (x3 + cos x)−4

A:

Q: Use the General Power Rule, Exponential Rule, or the Chain Rule to compute the derivative. y = ex−12

A:

Q: Use the Product Rule or the Quotient Rule to find the derivative of the function y = sin x/x4

A: ddxxn=n xn-1 Quotient rule f(x)g(x)'=f'(x)g(x)-g'(x)f(x)g(x)2

Q: Determine the derivative of the following function. f(x)=1+x^2/cotx=(1+x^2)tanx

A:

Q: Find the derivative of y = etanx

A:

Q: Use the Product Rule or the Quotient Rule to find the derivative of the function y = x4/cos x

A: Given function: y=x4cosx Recall Product Rule ddxmn=mddxn+nddxm…

Q: Determine the derivative of the given function by using two different methods

A: Given,         y=x2-3x2+34

Q: Calculate the derivative of the function below using the quotient rule. 28 y = Va + 8x7

A: We have given a function and we have to find its derivative using quotient rule.

Q: Find the most general anti-derivative

A:

Q: Find the portial derivative of

A: Follow 2nd step.

Q: find the derivative of y with respect to the givenindependent variable. y = log25 ex - log5 √x

A:

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

A: Given: y=ex tan x To Find: dydx=?

Q: Find the derivative and simplify: f(x)=ex-cotx

A: To determine the derivative.

Q: Calculate the derivative of h(x)= square root of x+1 when x=8 using alternate difference quotient

A: derivative of h(x)= square root of x+1 when x=8 using alternate difference quotient

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 of the function. Simplify wherepossible  x lnarctan x

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