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Popular Calculus >

derivative of 9cos(x-cos(9x))

Solution

\frac{d}{d x} (9 cos (x) - cos (9 x))

Solution

- 9 sin (x) + 9 sin (9 x)

Solution steps

\frac{d}{d x} (9 cos (x) - cos (9 x))

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d x} (9 cos (x)) - \frac{d}{d x} (cos (9 x))

\frac{d}{d x} (9 cos (x)) = - 9 sin (x)

\frac{d}{d x} (cos (9 x)) = - sin (9 x) \cdot 9

= - 9 sin (x) - (- sin (9 x) \cdot 9)

Simplify

= - 9 sin (x) + 9 sin (9 x)

Graph

Popular Examples

limit as x approaches 0 of 1/(1+x)

x \to 0 lim (\frac{1}{1 + x})

derivative of-5e^{-x}+30e^{-5x}

d er i v a t i v e - 5 e^{- x} + 30 e^{- 5 x}

integral of (1-3t)/(t^2)

\int \frac{1 - 3 t}{t ^{2}} d t

derivative of f(x)=15e^{x^2}

d er i v a t i v e f (x) = 15 e^{x^{2}}

derivative of f(x)=3x^2+12

d er i v a t i v e f (x) = 3 x^{2} + 12

Frequently Asked Questions (FAQ)

What is the derivative of 9cos(x-cos(9x)) ?
The derivative of 9cos(x-cos(9x)) is -9sin(x)+9sin(9x)
What is the first derivative of 9cos(x-cos(9x)) ?
The first derivative of 9cos(x-cos(9x)) is -9sin(x)+9sin(9x)