en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of f(x)=xcos(x)sin(x)

Solution

derivative of

f (x) = x cos (x) sin (x)

Solution

cos (x) sin (x) + x cos (2 x)

Solution steps

\frac{d}{d x} (x cos (x) sin (x))

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x, g = cos (x) sin (x)

= \frac{d x}{d x} cos (x) sin (x) + \frac{d}{d x} (cos (x) sin (x)) x

\frac{d x}{d x} = 1

\frac{d}{d x} (cos (x) sin (x)) = cos (2 x)

= 1 \cdot cos (x) sin (x) + cos (2 x) x

Simplify

= cos (x) sin (x) + x cos (2 x)

Popular Examples

integral from 0 to 1 of 1/(t^2+2)

\int_{0}^{1} \frac{1}{t ^{2} + 2} d t

x^4+y^3sqrt(x^5+4)(dy)/(dx)=0

x^{4} + y^{3} x^{5} + 4 \frac{d y}{d x} = 0

integral of (sin(3x))/(cos^3(3x))

\int \frac{sin ( 3 x )}{cos ^{3} ( 3 x )} d x

integral of 1/(6x^7)

\int \frac{1}{6 x ^{7}} d x

derivative of 4sqrt(x+1)

\frac{d}{d x} (4 x + 1)

Frequently Asked Questions (FAQ)

What is the derivative of f(x)=xcos(x)sin(x) ?
The derivative of f(x)=xcos(x)sin(x) is cos(x)sin(x)+xcos(2x)
What is the first derivative of f(x)=xcos(x)sin(x) ?
The first derivative of f(x)=xcos(x)sin(x) is cos(x)sin(x)+xcos(2x)