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Popular >

derivative of arccos(sin(x^2+9x))

Solution

\frac{d}{d x} (arccos (sin (x^{2} + 9 x)))

Solution

- 2 x - 9

Solution steps

\frac{d}{d x} (arccos (sin (x^{2} + 9 x)))

Apply the chain rule:

- \frac{1}{1 - ( sin ( x ^{2} + 9 x ) ) ^{2}} \frac{d}{d x} (sin (x^{2} + 9 x))

= - \frac{1}{1 - ( sin ( x ^{2} + 9 x ) ) ^{2}} \frac{d}{d x} (sin (x^{2} + 9 x))

\frac{d}{d x} (sin (x^{2} + 9 x)) = cos (x^{2} + 9 x) (2 x + 9)

= - \frac{1}{1 - ( sin ( x ^{2} + 9 x ) ) ^{2}} cos (x^{2} + 9 x) (2 x + 9)

Simplify

- \frac{1}{1 - sin ^{2} ( x ^{2} + 9 x )} cos (x^{2} + 9 x) (2 x + 9) : - 2 x - 9

= - 2 x - 9

Popular Examples

derivative of f(x)=sqrt(3x+4)derivative of

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limit as x approaches 0 of (1+3/x)^x

x \to 0 lim ((1 + \frac{3}{x})^{x})

tangent of f(x)= 2/(4-x),\at x=1 tangent of

f (x) = \frac{2}{4 - x}, at x = 1

integral from 0 to 1 of cos((pit)/2)

\int_{0}^{1} cos (\frac{π t}{2}) d t

limit as x approaches infinity of e^{-s(x)}

x \to \infty lim (e^{- s (x)})

Frequently Asked Questions (FAQ)

What is the derivative of arccos(sin(x^2+9x)) ?
The derivative of arccos(sin(x^2+9x)) is -2x-9
What is the first derivative of arccos(sin(x^2+9x)) ?
The first derivative of arccos(sin(x^2+9x)) is -2x-9