-f (x) = e* In(5x) – et"+2 + log find f '(1) .

Q: Differentiate: f(x) = 2ª + e² + log, 5 f'(x) = 2" In 2+ e² A 1 ® f'(x)= 2" +e² + : 1 © f'(x)= 2" +…

A:

Q: If f(x) = x + VT, find f' (1)

A:

Q: Suppose that f(x) = log4 (4x + 1). Find f' (2). f' (2) =

A:

Q: 7. f(x) = 6e* + log2(7x² + 3x + 1) f'(x) =

A: Given: fx=6ex+log27x2+3x+1 Differentiating fx with respect to x, f'x=ddx6ex+log27x2+3x+1…

Q: Find f''(x) if f(x) = e^3x^2+1.

A: calculate the second derivative for the given function

Q: If f(x) = 6x'n (=), find f'(2).

A: We first take ln on both sides and expand the right side

Q: Let f(x) = log2x and g(x) = log16x: Simplify the quotient f'(2x) g'(x)

A:

Q: Find h' (2) if h(x) = 1n(x + √(x2 - 1)) h'(2) =

A: Given hx=lnx+x2-1

Q: Find the derivative of f( x ) = log3(x + 6.5). f'(x) =

A:

Q: Let f(x) = e³x²(9x − 2). Compute f'(x). f'(x) =

A:

Q: S(x)=5?x®+log,x 2.x3+log,x Find f'(x)

A:

Q: Let f(x) = log, (8x? 3x + 10). Find f' (x).

A: Differentiation wrt x

Q: Find f’(e) of the following function. f(x)= x3 *(ln x- 1/3)

A:

Q: uppose ƒ(x) = 9* log5 (x). Find: -¹'(x) = ote: Enter In(a) In(h) for log, (a).

A:

Q: What is f’(2) for the function attached below?

A: We have to calculate the derivative of the given function at x=2 f'(2)…

Q: consider the function f(x)=e^6x g(x), where g(0)=-3, and g'(0)=-2 find f'(0)=

A:

Q: Consider h(x)= {3x^2 +1, if x3. What is h'(3)?

A:

Q: Find f'(z) of f(z) = Log(z2i).

A: Given complex function is  f(z)=log(z2i)

Q: Let g(x) = log3(æ). Find g'(4). g '(4).

A:

Q: If f(x) = (3x + 8), find f'(x). %3D Find f'(1).

A: Note some formule:

Q: Let f(x) = – 51log, (x) f'(x) f'(6) =

A:

Q: find f'(t) for f(x)=x/8x-8

A: We will need the quotient formula to find f'(x) Assume u and v, then find u' and v'

Q: If f(x) = log12(V3x* + x² + 4), find f'(x). Use exact values. f'(x) =

A:

Q: Q3: find the derivative of In(x4+3x-1) a) f(x) = %3D x²+1 b) f(x) = 4x³ . log(x² + 2x) %3D c) f(x) =…

A: Use product rule of differentiation.

Q: here y=f(x). f^-1(y)=

A: Let y=f(x)      f-1(y)=x Here f(x)=log(x24)

Q: Let g(s)=(e^s)/s+1. Find g''(s).

A: At the outset, I want to spell out that the way you have written g(s), it can have one of the two…

Q: In the equation f (x) = e* In(5x) – e**+2 + log(e2x^), find f'(3).

A:

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.