What is (\partial)/(\partial x)(2^{x+3y}) ?

The answer to (\partial)/(\partial x)(2^{x+3y}) is ln(2)*2^{x+3y}

Popular >

(\partial)/(\partial x)(2^{x+3y})

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

ln (2) \cdot 2^{x + 3 y}

Solution steps

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

Treat

y

as a constant

Apply exponent rule:

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

2^{x + 3 y} = e^{(x + 3 y) l n (2)}

= \frac{\partial}{\partial x} (e^{(x + 3 y) l n (2)})

Apply the chain rule:

e^{(x + 3 y) l n (2)} \frac{\partial}{\partial x} ((x + 3 y) ln (2))

= e^{(x + 3 y) l n (2)} \frac{\partial}{\partial x} ((x + 3 y) ln (2))

\frac{\partial}{\partial x} ((x + 3 y) ln (2)) = ln (2)

= e^{(x + 3 y) l n (2)} ln (2)

e^{(x + 3 y) l n (2)} = 2^{x + 3 y}

= ln (2) \cdot 2^{x + 3 y}

\frac{12}{x ^{2}}, - 24 x + 36, 0

\int \frac{2 x + 3}{1 + x ^{2}} d x

\int_{0}^{2} \frac{1}{1 + x ^{2}} d x

\frac{d}{d x} (\frac{e ^{x}}{2 x})

\frac{d y}{d x} = 500 e^{\frac{1}{10} l n (\frac{625}{500}) 50}

What is (\partial)/(\partial x)(2^{x+3y}) ?
The answer to (\partial)/(\partial x)(2^{x+3y}) is ln(2)*2^{x+3y}