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

The derivative of (tan(x)^{e^x}) is tan^{e^x}(x)(e^xln(tan(x))+2e^xcsc(2x))

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

The first derivative of (tan(x)^{e^x}) is tan^{e^x}(x)(e^xln(tan(x))+2e^xcsc(2x))

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

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

Solution steps

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

Apply exponent rule:

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

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

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

Apply the chain rule:

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

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

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

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

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

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

\int x^{2} 5 x + 6 d x

x \to 0 lim (C e^{- 4 x})

x \to - 1 lim (\frac{x ^{2} + 1}{x})

\frac{d}{d x} (\frac{x y}{x ^{2} + y ^{2}})

\int t^{3} e^{t^{4}} d t

What is the derivative of (tan(x)^{e^x}) ?
The derivative of (tan(x)^{e^x}) is tan^{e^x}(x)(e^xln(tan(x))+2e^xcsc(2x))
What is the first derivative of (tan(x)^{e^x}) ?
The first derivative of (tan(x)^{e^x}) is tan^{e^x}(x)(e^xln(tan(x))+2e^xcsc(2x))