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

The derivative of (sin(x)^{tan(x)}) is sin^{tan(x)}(x)(1+sec^2(x)ln(sin(x)))

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

The first derivative of (sin(x)^{tan(x)}) is sin^{tan(x)}(x)(1+sec^2(x)ln(sin(x)))

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

sin^{t a n (x)} (x) (1 + sec^{2} (x) ln (sin (x)))

Solution steps

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

Apply exponent rule:

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

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

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

Apply the chain rule:

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

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

\frac{d}{d x} (tan (x) ln (sin (x))) = 1 + sec^{2} (x) ln (sin (x))

= e^{t a n (x) l n (s i n (x))} (1 + sec^{2} (x) ln (sin (x)))

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

= sin^{t a n (x)} (x) (1 + sec^{2} (x) ln (sin (x)))

\int_{0}^{e} 2 π y (1 - ln (y)) d y

\int_{- 1}^{1} \frac{1}{2} x^{3} - 2 x + 2 d x

\int \frac{1}{x ^{3}} sin (\frac{1}{x}) d x

y^{^{''}} - 2 y^{^{'}} - 3 y = 24 t e^{2 t}, y (0) = 5, y^{^{'}} (0) = 0

d er i v a t i v e f (x) = \frac{1 + 3 x}{1 - 3 x}

What is the derivative of (sin(x)^{tan(x)}) ?
The derivative of (sin(x)^{tan(x)}) is sin^{tan(x)}(x)(1+sec^2(x)ln(sin(x)))
What is the first derivative of (sin(x)^{tan(x)}) ?
The first derivative of (sin(x)^{tan(x)}) is sin^{tan(x)}(x)(1+sec^2(x)ln(sin(x)))