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

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

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

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

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derivative of

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

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

Solution steps

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

Apply exponent rule:

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

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

\int \frac{x}{2 x + 1} d x

x \to 2 lim ((3 - x) (x + 1))

\frac{\partial}{\partial x} (\frac{5}{x y} - 4 x^{2} - 2 y^{2})

\int \frac{1}{x ^{2} - 4 x + 8} d x

f (x) = (x)^{3}

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