What is the derivative of f(x)=pi^{x^2} ?

The derivative of f(x)=pi^{x^2} is 2ln(pi)pi^{x^2}x

What is the first derivative of f(x)=pi^{x^2} ?

The first derivative of f(x)=pi^{x^2} is 2ln(pi)pi^{x^2}x

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derivative of

f (x) = π^{x^{2}}

2 ln (π) π^{x^{2}} x

Solution steps

\frac{d}{d x} (π^{x^{2}})

Apply exponent rule:

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

π^{x^{2}} = e^{x^{2} l n (π)}

= \frac{d}{d x} (e^{x^{2} l n (π)})

Apply the chain rule:

e^{x^{2} l n (π)} \frac{d}{d x} (x^{2} ln (π))

= e^{x^{2} l n (π)} \frac{d}{d x} (x^{2} ln (π))

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

= e^{x^{2} l n (π)} \cdot 2 ln (π) x

e^{x^{2} l n (π)} = π^{x^{2}}

= 2 ln (π) π^{x^{2}} x

y^{^{'}} = 2

\int 8 x^{- 5} d x

\int \frac{1}{x ^{2} + 100} d x

t y^{^{'}} = 2 y + 2 t^{3} sin (3 t), y (\frac{π}{3}) = 0

What is the derivative of f(x)=pi^{x^2} ?
The derivative of f(x)=pi^{x^2} is 2ln(pi)pi^{x^2}x
What is the first derivative of f(x)=pi^{x^2} ?
The first derivative of f(x)=pi^{x^2} is 2ln(pi)pi^{x^2}x