en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of sin^2(xcos^2(x))

Solution

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

Solution

\frac{sin ( 4 x )}{2}

Solution steps

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

Apply the Product Rule:

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

f = sin^{2} (x), g = cos^{2} (x)

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

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

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

= sin (2 x) cos^{2} (x) + (- sin (2 x)) sin^{2} (x)

Simplify

sin (2 x) cos^{2} (x) + (- sin (2 x)) sin^{2} (x) : \frac{sin ( 4 x )}{2}

= \frac{sin ( 4 x )}{2}

Popular Examples

derivative of (2x^2+4x-3/(x-5))

\frac{d}{d x} (\frac{2 x ^{2} + 4 x - 3}{x - 5})

derivative of e^{-9x}derivative of

e^{- 9 x}

derivative of sec^2(6x)

\frac{d}{d x} (sec^{2} (6 x))

derivative of c_{1}e^x+c_{2}e^{2x}

\frac{d}{d x} (c_{1} e^{x} + c_{2} e^{2 x})

(dx}{dt}=t^5-\frac{2x)/t

\frac{d x}{d t} = t^{5} - \frac{2 x}{t}

Frequently Asked Questions (FAQ)

What is the derivative of sin^2(xcos^2(x)) ?
The derivative of sin^2(xcos^2(x)) is (sin(4x))/2
What is the first derivative of sin^2(xcos^2(x)) ?
The first derivative of sin^2(xcos^2(x)) is (sin(4x))/2