What is the derivative of x^{tan(x)} ?

The derivative of x^{tan(x)} is e^{tan(x)ln(x)}(sec^2(x)ln(x)+(tan(x))/x)

What is the first derivative of x^{tan(x)} ?

The first derivative of x^{tan(x)} is e^{tan(x)ln(x)}(sec^2(x)ln(x)+(tan(x))/x)

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derivative of

x^{t a n (x)}

e^{t a n (x) l n (x)} (sec^{2} (x) ln (x) + \frac{tan ( x )}{x})

Solution steps

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

Apply exponent rule:

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

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

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

Apply the chain rule:

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

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

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

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

\frac{d y}{d x} = cos (y - x)

\int_{0}^{N} e^{- s t} sin (5 t) d t

\frac{1}{s ( 2 s + 1 )}

\frac{d}{d x} (se x + cos (x))

\int 2 x (x^{2} + 1)^{6} d x

What is the derivative of x^{tan(x)} ?
The derivative of x^{tan(x)} is e^{tan(x)ln(x)}(sec^2(x)ln(x)+(tan(x))/x)
What is the first derivative of x^{tan(x)} ?
The first derivative of x^{tan(x)} is e^{tan(x)ln(x)}(sec^2(x)ln(x)+(tan(x))/x)