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Popular >

derivative of 1/5 cos(5x)

Solution

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

Solution

- sin (5 x)

Solution steps

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

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply the chain rule:

- sin (5 x) \frac{d}{d x} (5 x)

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

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

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

Simplify

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

= - sin (5 x)

Popular Examples

integral from 1200 to 1204 of 0.1

\int_{1200}^{1204} 0.1 d x

integral of 5x^{1/3}+2x^{-1/3}+11

\int 5 x^{\frac{1}{3}} + 2 x^{- \frac{1}{3}} + 11 d x

integral of (x+1)/(x^2-4x+8)

\int \frac{x + 1}{x ^{2} - 4 x + 8} d x

integral from-1 to 2 of (2-y^2)-(-y)

\int_{- 1}^{2} (2 - y^{2}) - (- y) d y

sum from n=0 to infinity of 10(1/3)^n

n = 0 \sum \infty 10 (\frac{1}{3})^{n}

Frequently Asked Questions (FAQ)

What is the derivative of 1/5 cos(5x) ?
The derivative of 1/5 cos(5x) is -sin(5x)
What is the first derivative of 1/5 cos(5x) ?
The first derivative of 1/5 cos(5x) is -sin(5x)