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

The derivative of (tan(x)^{sin(x)}) is tan^{sin(x)}(x)(cos(x)ln(tan(x))+sec(x))

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

The first derivative of (tan(x)^{sin(x)}) is tan^{sin(x)}(x)(cos(x)ln(tan(x))+sec(x))

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\frac{d}{d x} ((tan (x))^{s i n (x)})

tan^{s i n (x)} (x) (cos (x) ln (tan (x)) + sec (x))

Solution steps

\frac{d}{d x} ((tan (x))^{s i n (x)})

Apply exponent rule:

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

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

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

Apply the chain rule:

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

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

\frac{d}{d x} (sin (x) ln (tan (x))) = cos (x) ln (tan (x)) + sec (x)

= e^{s i n (x) l n (t a n (x))} (cos (x) ln (tan (x)) + sec (x))

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

= tan^{s i n (x)} (x) (cos (x) ln (tan (x)) + sec (x))

\frac{d}{d x} (- 2 e^{2 x})

x \to 6 lim (\frac{7}{x - 6})

\int_{0}^{4} 2 x^{2} - 7 x + 3 d x

(\frac{d y}{d x}) + \frac{2 x y}{x ^{2} + 1} = x

f (x) = - (\frac{1}{3})^{(x + 2)}

What is the derivative of (tan(x)^{sin(x)}) ?
The derivative of (tan(x)^{sin(x)}) is tan^{sin(x)}(x)(cos(x)ln(tan(x))+sec(x))
What is the first derivative of (tan(x)^{sin(x)}) ?
The first derivative of (tan(x)^{sin(x)}) is tan^{sin(x)}(x)(cos(x)ln(tan(x))+sec(x))