What is (\partial)/(\partial x)(2^x+2^y) ?

The answer to (\partial)/(\partial x)(2^x+2^y) is ln(2)*2^x

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

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

ln (2) \cdot 2^{x}

Solution steps

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

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

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

\frac{\partial}{\partial x} (2^{x}) = 2^{x} ln (2)

\frac{\partial}{\partial x} (2^{y}) = 0

= 2^{x} ln (2) + 0

Simplify

= ln (2) \cdot 2^{x}

\frac{\partial}{\partial x} (3 x^{2} - 6 x + 3 y^{2})

\int x^{2} e d x

l a pl a ce t r an s f or m sin (100 \cdot t)

8 y^{^{''}} - 8 y^{^{'}} + 52 y = 0

d er i v a t i v e f (x) = \frac{x ^{2} + 1}{x}

What is (\partial)/(\partial x)(2^x+2^y) ?
The answer to (\partial)/(\partial x)(2^x+2^y) is ln(2)*2^x