What is the derivative of x^{-9cos(x}) ?

The derivative of x^{-9cos(x}) is x^{-9cos(x)}(9sin(x)ln(x)-(9cos(x))/x)

What is the first derivative of x^{-9cos(x}) ?

The first derivative of x^{-9cos(x}) is x^{-9cos(x)}(9sin(x)ln(x)-(9cos(x))/x)

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\frac{d}{d x} (x^{- 9 c o s (x)})

x^{- 9 c o s (x)} (9 sin (x) ln (x) - \frac{9 cos ( x )}{x})

Solution steps

\frac{d}{d x} (x^{- 9 c o s (x)})

Apply exponent rule:

a^{b} = e^{b l n (a)}

x^{- 9 c o s (x)} = e^{(- 9 c o s (x)) l n (x)}

= \frac{d}{d x} (e^{(- 9 c o s (x)) l n (x)})

Apply the chain rule:

e^{(- 9 c o s (x)) l n (x)} \frac{d}{d x} ((- 9 cos (x)) ln (x))

= e^{(- 9 c o s (x)) l n (x)} \frac{d}{d x} ((- 9 cos (x)) ln (x))

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

= e^{(- 9 c o s (x)) l n (x)} (9 sin (x) ln (x) - \frac{9 cos ( x )}{x})

Simplify

e^{(- 9 c o s (x)) l n (x)} (9 sin (x) ln (x) - \frac{9 cos ( x )}{x}) : x^{- 9 c o s (x)} (9 sin (x) ln (x) - \frac{9 cos ( x )}{x})

= x^{- 9 c o s (x)} (9 sin (x) ln (x) - \frac{9 cos ( x )}{x})

3 \frac{d y}{d t} = y - t^{2} y

\frac{\partial}{\partial x} (cos (4 y - 3 x))

\int sin (x) tan^{2} (x) d x

\frac{\partial}{\partial x} (x^{2} - 2 x)

What is the derivative of x^{-9cos(x}) ?
The derivative of x^{-9cos(x}) is x^{-9cos(x)}(9sin(x)ln(x)-(9cos(x))/x)
What is the first derivative of x^{-9cos(x}) ?
The first derivative of x^{-9cos(x}) is x^{-9cos(x)}(9sin(x)ln(x)-(9cos(x))/x)