What is the derivative of sin^{-5}(x-cos^3(x)) ?

The derivative of sin^{-5}(x-cos^3(x)) is -(5cos(x))/(sin^6(x))+3cos^2(x)sin(x)

What is the first derivative of sin^{-5}(x-cos^3(x)) ?

The first derivative of sin^{-5}(x-cos^3(x)) is -(5cos(x))/(sin^6(x))+3cos^2(x)sin(x)

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Popular >

\frac{d}{d x} (sin^{- 5} (x) - cos^{3} (x))

- \frac{5 cos ( x )}{sin ^{6} ( x )} + 3 cos^{2} (x) sin (x)

Solution steps

\frac{d}{d x} (sin^{- 5} (x) - cos^{3} (x))

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (sin^{- 5} (x)) - \frac{d}{d x} (cos^{3} (x))

\frac{d}{d x} (sin^{- 5} (x)) = - \frac{5 cos ( x )}{sin ^{6} ( x )}

\frac{d}{d x} (cos^{3} (x)) = - 3 cos^{2} (x) sin (x)

= - \frac{5 cos ( x )}{sin ^{6} ( x )} - (- 3 cos^{2} (x) sin (x))

Simplify

= - \frac{5 cos ( x )}{sin ^{6} ( x )} + 3 cos^{2} (x) sin (x)

\int \frac{( x + 1 )}{x} d x

(csc^{2} (x))^{^{'}}

\int \frac{x}{25 - x ^{2}} d x

\frac{d y}{d x}, y^{3} = x^{2}

\frac{d}{d x} (2 x^{3} + 3 x^{2} - 12 x + 5)

What is the derivative of sin^{-5}(x-cos^3(x)) ?
The derivative of sin^{-5}(x-cos^3(x)) is -(5cos(x))/(sin^6(x))+3cos^2(x)sin(x)
What is the first derivative of sin^{-5}(x-cos^3(x)) ?
The first derivative of sin^{-5}(x-cos^3(x)) is -(5cos(x))/(sin^6(x))+3cos^2(x)sin(x)