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

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

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

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

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derivative of

cos^{s i n (x)} (x)

cos^{s i n (x)} (x) (cos (x) ln (cos (x)) - tan (x) sin (x))

Solution steps

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

Apply exponent rule:

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

cos^{s i n (x)} (x) = e^{s i n (x) l n (c o s (x))}

= \frac{d}{d x} (e^{s i n (x) l n (c o s (x))})

Apply the chain rule:

e^{s i n (x) l n (c o s (x))} \frac{d}{d x} (sin (x) ln (cos (x)))

= e^{s i n (x) l n (c o s (x))} \frac{d}{d x} (sin (x) ln (cos (x)))

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

= e^{s i n (x) l n (c o s (x))} (cos (x) ln (cos (x)) - tan (x) sin (x))

e^{s i n (x) l n (c o s (x))} = cos^{s i n (x)} (x)

= cos^{s i n (x)} (x) (cos (x) ln (cos (x)) - tan (x) sin (x))

f (x) = e^{- 0.5 x} (4 - x) - 2

n = 1 \sum \infty \frac{5}{4 n ^{2} - 1}

\frac{d}{d x} (- 3 sin (6 x))

3 x, \frac{6 x}{7}, 55 - x^{2}

\frac{\partial}{\partial t} (e^{- t} cos (t))

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