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Popular >

derivative of f(x)=x^{pi^2}+(pi^2)^x

Solution

derivative of

f (x) = x^{π^{2}} + (π^{2})^{x}

Solution

π^{2} x^{π^{2} - 1} + 2 ln (π) π^{2 x}

Solution steps

\frac{d}{d x} (x^{π^{2}} + (π^{2})^{x})

Simplify

x^{π^{2}} + (π^{2})^{x} : x^{π^{2}} + π^{2 x}

= \frac{d}{d x} (x^{π^{2}} + π^{2 x})

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

\frac{d}{d x} (x^{π^{2}}) = π^{2} x^{π^{2} - 1}

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

= π^{2} x^{π^{2} - 1} + 2 ln (π) π^{2 x}

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(\partial)/(\partial x)(x^3ln(y^2))

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Frequently Asked Questions (FAQ)

What is the derivative of f(x)=x^{pi^2}+(pi^2)^x ?
The derivative of f(x)=x^{pi^2}+(pi^2)^x is pi^2x^{pi^2-1}+2ln(pi)pi^{2x}
What is the first derivative of f(x)=x^{pi^2}+(pi^2)^x ?
The first derivative of f(x)=x^{pi^2}+(pi^2)^x is pi^2x^{pi^2-1}+2ln(pi)pi^{2x}