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Popular Calculus >

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

Graph

Popular Examples

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d er i v a t i v e f (x) = 3 x + 4

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

t an g e n t f (x) = \frac{2}{4 - x}, at x = 1

derivative of (x-2^{-1})

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

implicit 7x^2-y^2=4

im pl i c i t 7 x^{2} - y^{2} = 4

area y=x^3,y=8,x=-1

a re a y = x^{3}, y = 8, x = - 1

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