Explained: "Use exponential and logarithmic differentiation to find the..." - Plainmath

Kyran Hudson

Answered question

2021-10-18

Use exponential and logarithmic differentiation to find the derivatives of the following function:

5 x^{x - 3}

Answer & Explanation

Anonym

Skilled2021-10-19Added 108 answers

Step 1
Given,

5 x^{x - 3}

Step 2
Taking logrithmic on both sides

\ln y = \ln (5 x^{x - 3})

Using the product rule of the derivative.

\frac{1}{y} \frac{d y}{d x} = (x - 3) \frac{d}{d x} (\ln (5 x)) + (\ln (5 x)) \frac{d}{d x} (x - 3)

\frac{1}{y} \frac{d y}{d x} = (x - 3) (\frac{1}{5 x} (5)) + (\ln (5 x)) (1)

\frac{1}{y} \frac{d y}{d x} = (x - 3) (\frac{1}{x}) + \ln (5 x)

\frac{1}{y} \frac{d y}{d x} = \frac{(x - 3)}{x} + \ln (5 x)

\frac{d y}{d x} = y [\frac{(x - 3)}{x} + \ln (5 x)]

\frac{d y}{d x} = 5 x^{x - 3} [\frac{(x - 3)}{x} + \ln (5 x)]

Do you have a similar question?

Recalculate according to your conditions!

New Questions in Differential Calculus

What is the Mixed Derivative Theorem for mixed second-order partial derivatives? How can it help in calculating partial derivatives of second and higher orders?
How do I find the y-intercept of a parabola?
What are the vertices of $9 x^{2} + 16 y^{2} = 144$ ?
How to determine the rate of change of a function?
Why are the tangents for 90 and 270 degrees undefined?
How to find the center and radius of the circle $x^{2} + y^{2} - 6 x + 8 y = 0$ ?
What is multiplicative inverse of a number?
How to find the continuity of a function on a closed interval?
How do I find the tangent line of a function?
How to find vertical asymptotes using limits?
How to find the center and radius of the circle $x^{2} - 12 x + y^{2} + 4 y + 15 = 0$ ?
Let f be a function so that (below). Which must be true?
I. f is continuous at x=2
II. f is differentiable at x=2
III. The derivative of f is continuous at x=2
(A) I (B) II (C) I and II (D) I and III (E) II and III
How to find the center and radius of the circle given $x^{2} + y^{2} + 8 x - 6 y = 0$ ?
How to find the center and radius of the circle $x^{2} + y^{2} + 4 x - 8 y + 4 = 0$ ?
How to identify the center and radius of the circle ${(x + 3)}^{2} + {(y - 8)}^{2} = 16$ ?

Didn't find what you were looking for?