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))

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

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))

sin (\frac{π}{x})

12 y y^{^{'}} - 7 e^{x} = 0

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

\int \frac{1}{( x + 4 ) ( x - 1 )} d x

y = e^{x}, y = e^{- 3 x}, x = ln (5)

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))