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Popular >

derivative of (tan(x)^x)

Solution

\frac{d}{d x} ((tan (x))^{x})

Solution

tan^{x} (x) (ln (tan (x)) + 2 x csc (2 x))

Solution steps

\frac{d}{d x} ((tan (x))^{x})

Apply exponent rule:

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

(tan (x))^{x} = e^{x l n (t a n (x))}

= \frac{d}{d x} (e^{x l n (t a n (x))})

Apply the chain rule:

e^{x l n (t a n (x))} \frac{d}{d x} (x ln (tan (x)))

= e^{x l n (t a n (x))} \frac{d}{d x} (x ln (tan (x)))

\frac{d}{d x} (x ln (tan (x))) = ln (tan (x)) + 2 x csc (2 x)

= e^{x l n (t a n (x))} (ln (tan (x)) + 2 x csc (2 x))

e^{x l n (t a n (x))} = tan^{x} (x)

= tan^{x} (x) (ln (tan (x)) + 2 x csc (2 x))

Graph

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Frequently Asked Questions (FAQ)

What is the derivative of (tan(x)^x) ?
The derivative of (tan(x)^x) is tan^x(x)(ln(tan(x))+2xcsc(2x))
What is the first derivative of (tan(x)^x) ?
The first derivative of (tan(x)^x) is tan^x(x)(ln(tan(x))+2xcsc(2x))