Expert Answer to "Find the derivative of x 3 cos..."

College
Calculus and Analysis
Differential Calculus
Derivatives

Reese Estes

Answered question

2022-05-05

Find the derivative of

x^{3} ﻿ \cos (π x)

Answer & Explanation

charringpq49u

Beginner2022-05-06Added 23 answers

Differentiate using the Product Rule which states that $\frac{d}{d x} [f (x) g (x)]$ is $f (x) \frac{d}{d x} [g (x)] + g (x) \frac{d}{d x} [f (x)]$ where $f (x) = x^{3}$ and $g (x) = \cos (π x)$ .

$x^{3} \frac{d}{d x} [\cos (π x)] + \cos (π x) \frac{d}{d x} [x^{3}]$

Differentiate using the chain rule, which states that $\frac{d}{d x} [f (g (x))]$ is $f' (g (x)) g' (x)$ where $f (x) = \cos (x)$ and $g (x) = π x$ .

$x^{3} (- \sin (π x) \frac{d}{d x} [π x]) + \cos (π x) \frac{d}{d x} [x^{3}]$

Differentiate.

$- π x^{3} \sin (π x) + 3 x^{2} \cos (π x)$

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?