en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of sqrt(cos(5x))

Solution

\frac{d}{d x} (cos (5 x))

Solution

- \frac{5 sin ( 5 x )}{2 cos ( 5 x )}

Solution steps

\frac{d}{d x} (cos (5 x))

Apply the chain rule:

\frac{1}{2 cos ( 5 x )} \frac{d}{d x} (cos (5 x))

= \frac{1}{2 cos ( 5 x )} \frac{d}{d x} (cos (5 x))

\frac{d}{d x} (cos (5 x)) = - sin (5 x) \cdot 5

= \frac{1}{2 cos ( 5 x )} (- sin (5 x) \cdot 5)

Simplify

\frac{1}{2 cos ( 5 x )} (- sin (5 x) \cdot 5) : - \frac{5 sin ( 5 x )}{2 cos ( 5 x )}

= - \frac{5 sin ( 5 x )}{2 cos ( 5 x )}

Popular Examples

integral from 0 to pi/2 of 5cos^5(x)

\int_{0}^{\frac{π}{2}} 5 cos^{5} (x) d x

integral from 0 to 1 of sqrt(1+(6\sqrt{x))^2}

\int_{0}^{1} 1 + (6 x)^{2} d x

integral of (x^2-4x+3)/(x^3+2x^2+x)

\int \frac{x ^{2} - 4 x + 3}{x ^{3} + 2 x ^{2} + x} d x

(\partial)/(\partial x)(x+y+xy)

\frac{\partial}{\partial x} (x + y + x y)

limit as z approaches 2 of sqrt(7z^2+14z-7)

z \to 2 lim (7 z^{2} + 14 z - 7)

Frequently Asked Questions (FAQ)

What is the derivative of sqrt(cos(5x)) ?
The derivative of sqrt(cos(5x)) is -(5sin(5x))/(2sqrt(cos(5x)))
What is the first derivative of sqrt(cos(5x)) ?
The first derivative of sqrt(cos(5x)) is -(5sin(5x))/(2sqrt(cos(5x)))