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

The derivative of pi^{xtan(x}) is ln(pi)pi^{xtan(x)}(tan(x)+xsec^2(x))

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

The first derivative of pi^{xtan(x}) is ln(pi)pi^{xtan(x)}(tan(x)+xsec^2(x))

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\frac{d}{d x} (π^{x t a n (x)})

ln (π) π^{x t a n (x)} (tan (x) + x sec^{2} (x))

Solution steps

\frac{d}{d x} (π^{x t a n (x)})

Apply exponent rule:

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

π^{x t a n (x)} = e^{x t a n (x) l n (π)}

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

Apply the chain rule:

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

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

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

= e^{x t a n (x) l n (π)} ln (π) (tan (x) + x sec^{2} (x))

e^{x t a n (x) l n (π)} = π^{x t a n (x)}

= ln (π) π^{x t a n (x)} (tan (x) + x sec^{2} (x))

g (x) = x arcsinh (x) - 1 + x^{2}

\frac{1}{( s + 3 ) ^{4}}

\int 36 x (2 x^{2} - 5)^{8} d x

\frac{2 s + 1}{s ( s + 1 ) ^{2}}

\frac{d x}{d t} = \frac{( e ^{t} - e ^{- t} )}{3 + x}, x (0) = 0

What is the derivative of pi^{xtan(x}) ?
The derivative of pi^{xtan(x}) is ln(pi)pi^{xtan(x)}(tan(x)+xsec^2(x))
What is the first derivative of pi^{xtan(x}) ?
The first derivative of pi^{xtan(x}) is ln(pi)pi^{xtan(x)}(tan(x)+xsec^2(x))