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

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

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

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

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Popular >

\frac{d}{d x} (π^{c o s (x)})

- ln (π) π^{c o s (x)} sin (x)

Solution steps

\frac{d}{d x} (π^{c o s (x)})

Apply exponent rule:

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

π^{c o s (x)} = e^{c o s (x) l n (π)}

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

Apply the chain rule:

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

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

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

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

Simplify

e^{c o s (x) l n (π)} (- ln (π) sin (x)) : - ln (π) π^{c o s (x)} sin (x)

= - ln (π) π^{c o s (x)} sin (x)

x \to 0 lim ((\frac{x + 2}{x})^{2} - 4)

2^{20}

\int (10 x + 1) 5 x^{2} + x d x

\int x e^{- y} d y

\frac{d}{d x} (x^{4} - 5 x)

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