If f(x) = exg(x), where g(0) = 5 and g'(0) = 2, find f '(0).

Q: Find the derivative of the function.   f(x) = x5 ln(x)   f'(x)=

A: We have to find the derivative of function: fx=x5lnx Here there are two function in multiplication…

Q: Find the 5th derivative of the function y=x2sin2x at x=0.

A:

Q: Which function has the same derivative function f(x) as g(x) = lnx + x² – x?

A:

Q: Find the derivative of the function.…

A: The given function is hx=x2arctan8x

Q: Find the second derivative for the functions defined as follows g(x) = 4x(ln x)

A: We have to find second derivative of the function: gx=4x lnx Since two function are in product so we…

Q: Find the first derivative of y = e3x. 3e3x

A:

Q: Find the first derivative of the following functions Y = x5 e-3 ln x and Y = ln √ [ (x – 1 ) / ( x…

A: Solution is given below:

Q: By using logarithmic differentiation and with respect to independent variable x, find the derivative…

A:

Q: part ii, thank you very much.

A:

Q: Find the first derivative of y = (ln x)4

A: Given the  y = ( ln x)^4 We need to find the first derivative . Therefore differentiate to given…

Q: What is the first derivative of s(x) = 4e.

A: Given function - s(x) = 4ex-3Differentiating on both sides with respect to x - ddxs(x) =…

Q: y = ln 1-x² 1+x²

A:

Q: Which function has the same derivative function f (x) as g(x) = lnx + x² – x?

A: we have to find derivative

Q: x + x dx x2

A:

Q: find the second derivative of y=ln(e^x+e^-x)

A: Given query is to find the second derivative of the expression.

Q: Find the derivative of the function. h(x) = x2 arctan(5x)

A: Given function: hx=x2tan-15x Differentiate the above function w.r.t "X" h'x=ddxx2tan-15x

Q: Find the derivative of the function. y = (ln x)4

A:

Q: Find the derivative of the function.

A: Given y=lnx+1x-1

Q: Find the indicated derivative of the function. for y = -4 cos X dx4

A:

Q: Find the second derivative of the function. 3root(x) + e^(6x)ln(x)

A:

Q: Find the derivative of f (x) = 9ª ln (x).

A: Given: f(x)=9xln(x)

Q: If C(x)=x' + x°, evaluate the fourth derivative at x = 2. %3D

A: To find the fourth derivative of the function: C(x)=x5+x-3 at x=2

Q: Calculate the 4th derivative of the function y=x2/x−1 at x=2.

A:

Q: Determine the first derivative of the ff. function y = Vxe2* cos x

A: Derivative of a function gives the tangent of the curve at a given point. Derivatives are used to…

Q: Find the derivative of the function. h(x) = x² arctan(5x) h'(x) =

A: h(x)=x2tan-1(x)

Q: find the derivative of ln(3x^2+e^x)

A:

Q: Find the derivative of z=(ln5)e^x dz/dx=

A:

Q: Find the derivative of the function. y = x2 ln x2

A: Consider the provided question, We have to find the derivative of the given function,

Q: Find the first derivative of = (ln x)* 4 y

A: From the given function; y=lnx4 We know that; The Power law: ddxxn=nxn-1 The chain rule:…

Q: What is the derivative of: y ln x − x ln y = 1

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

Q: What is the first derivative of the expression (xy)× = e?

A: See the details solution in below

Q: Find the derivative of the function. f(x) = x6 ln(x)

A:

Q: Find the first And 2nd derivative  F(x)= e^x sin4x

A:

Q: Find the derivative of the function y, below. y = 6x(ln a + In 5) – 8x + e ||

A: Given that y=6x(lnx+ln5)-8x+e To find the derivative of y

Q: Find the derivative of the function  f(x)= e^-3x ln x

A: Given function is

Q: Find the derivative of the function h(x) = x2 arctan5x

A: The given function is h(x) = x2 arctan5x

Q: Find the derivative of the function. f(x) = ln(x − 1)

A:

Q: Find the derivative of the function. f(x) = ln(x2 + 3)

A:

Q: Find the equation of the tangent line to the graph of f(x) = 4^(x/ln2) at the point where x is ln16.

A: We find dy/dx to find the slope at x.

Q: Find the derivative of the function y, below. 9x(ln x + In 2) – 8x + v2 %3D

A: first, simplify the function  y=9xlnx+ln2-8x+2 y=9xlnx·2-8x+2 y=9xln2x-8x+2

Q: Find the derivative of the function. y = ln(x√x2 − 1 )

A:

Q: solve the first and second derivative of Y= (1+lnx)  /  x

A: If y=f(x), then the independent variable x is called the input of the function, and the dependent…

Q: Find the derivative of the function - 3x f(x) = 3 ln(x) + e - df dx

A:

Q: Find the derivative of f(x) = 4e 3x + e -x^2 f(x)= ?

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Q: find the first derivative in the form of dy/dx y=(3x-ln(x))^5

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Q: Find the differential of the function y=lntan2x at x=π/8.

A: Given: ,at x=π/8 Differentials are infinitely small quantities. Use the term for differentials as…

Q: Find the nth derivative of the function y=xlnx at x=1.

A:

Q: Find the derivative of f (x) =arcoth (e³" ).

A:

Q: Find the first derivative of:   f(x) = ln [(5x+2)1/2 / csc(x)]

A:

Q: Find the first derivative of x² + 3xy + y3 = 10 implicitly.

A: The given function x2+3xy+y3=10