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

The derivative of (cos(9x))^x is cos^x(9x)(ln(cos(9x))-9xtan(9x))

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

The first derivative of (cos(9x))^x is cos^x(9x)(ln(cos(9x))-9xtan(9x))

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derivative of

(cos (9 x))^{x}

cos^{x} (9 x) (ln (cos (9 x)) - 9 x tan (9 x))

Solution steps

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

Apply exponent rule:

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

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

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

Apply the chain rule:

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

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

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

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

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

= cos^{x} (9 x) (ln (cos (9 x)) - 9 x tan (9 x))

48 y^{^{''}} + 34 y^{^{'}} - 5 y = 0

\frac{d}{d x} ((4 x - 3)^{2})

x^{(\frac{4}{3})}, 2 x^{(\frac{1}{3})}, 0, 2

(e^{y} + 1)^{2} e^{- y} d x + (e^{x} + 1)^{5} e^{- x} d y = 0

\int \frac{sec ( x )}{sec ( x ) - tan ( x )} d x

What is the derivative of (cos(9x))^x ?
The derivative of (cos(9x))^x is cos^x(9x)(ln(cos(9x))-9xtan(9x))
What is the first derivative of (cos(9x))^x ?
The first derivative of (cos(9x))^x is cos^x(9x)(ln(cos(9x))-9xtan(9x))