en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of y=x^2cos^4(x)

Solution

derivative of

y = x^{2} cos^{4} (x)

Solution

2 x cos^{4} (x) - 4 x^{2} cos^{3} (x) sin (x)

Solution steps

\frac{d}{d x} (x^{2} cos^{4} (x))

Apply the Product Rule:

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

f = x^{2}, g = cos^{4} (x)

= \frac{d}{d x} (x^{2}) cos^{4} (x) + \frac{d}{d x} (cos^{4} (x)) x^{2}

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

\frac{d}{d x} (cos^{4} (x)) = - 4 cos^{3} (x) sin (x)

= 2 x cos^{4} (x) + (- 4 cos^{3} (x) sin (x)) x^{2}

Simplify

= 2 x cos^{4} (x) - 4 x^{2} cos^{3} (x) sin (x)

Popular Examples

integral of (tan(2x))

\int (tan (2 x)) d x

derivative of 1/8 (-x^2+8ln(x))

\frac{d}{d x} (\frac{1}{8} (- x^{2} + 8 ln (x)))

y^{''}+6y^'+25y=0,y(0)=2,y^'(0)=-5

y^{^{''}} + 6 y^{^{'}} + 25 y = 0, y (0) = 2, y^{^{'}} (0) = - 5

integral from 0 to 7 of k(7-x)

\int_{0}^{7} k (7 - x)

limit as t approaches+0 of 18(1.15)^t

t \to + 0 lim (18 (1.15)^{t})

Frequently Asked Questions (FAQ)

What is the derivative of y=x^2cos^4(x) ?
The derivative of y=x^2cos^4(x) is 2xcos^4(x)-4x^2cos^3(x)sin(x)
What is the first derivative of y=x^2cos^4(x) ?
The first derivative of y=x^2cos^4(x) is 2xcos^4(x)-4x^2cos^3(x)sin(x)