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Popular >

derivative of pi^{sqrt(x)}

Solution

\frac{d}{d x} (π^{x})

Solution

\frac{ln ( π ) π ^{x}}{2 x}

Solution steps

\frac{d}{d x} (π^{x})

Apply exponent rule:

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

π^{x} = e^{x l n (π)}

= \frac{d}{d x} (e^{x l n (π)})

Apply the chain rule:

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

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

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

= e^{x l n (π)} \frac{ln ( π )}{2 x}

Simplify

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

= \frac{ln ( π ) π ^{x}}{2 x}

Popular Examples

(\partial}{\partial x}(\frac{sin(x))/x)

\frac{\partial}{\partial x} (\frac{sin ( x )}{x})

y^{''}-2y^'+10y=0,y(0)=4,y^'(0)=1

y^{^{''}} - 2 y^{^{'}} + 10 y = 0, y (0) = 4, y^{^{'}} (0) = 1

limit as x approaches-9-of x^2+3/(x+9)

x \to - 9 - lim (x^{2} + \frac{3}{x + 9})

(\partial)/(\partial y)((-y)/(2x^2+y^2))

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

integral of (3z+z^2)sin(z)

\int (3 z + z^{2}) sin (z) d z

Frequently Asked Questions (FAQ)

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