What is (\partial)/(\partial x)(a^x-b^x) ?

The answer to (\partial)/(\partial x)(a^x-b^x) is a^xln(a)-b^xln(b)

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(\partial)/(\partial x)(a^x-b^x)

\frac{\partial}{\partial x} (a^{x} - b^{x})

a^{x} ln (a) - b^{x} ln (b)

Solution steps

\frac{\partial}{\partial x} (a^{x} - b^{x})

Treat

a, b

as a constant

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial x} (a^{x}) - \frac{\partial}{\partial x} (b^{x})

\frac{\partial}{\partial x} (a^{x}) = a^{x} ln (a)

\frac{\partial}{\partial x} (b^{x}) = b^{x} ln (b)

= a^{x} ln (a) - b^{x} ln (b)

\int t^{2} e^{- 22 t} d t

\int 1 - 7 x^{2} d x

n = 2 \sum \infty \frac{5}{2 ^{n}}

t e^{- 5 t}

5 t ln (t)

What is (\partial)/(\partial x)(a^x-b^x) ?
The answer to (\partial)/(\partial x)(a^x-b^x) is a^xln(a)-b^xln(b)