What is (\partial)/(\partial x)(sqrt(x+e^{4y)}) ?

The answer to (\partial)/(\partial x)(sqrt(x+e^{4y)}) is 1/(2sqrt(x+e^{4y))}

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(\partial)/(\partial x)(sqrt(x+e^{4y)})

\frac{\partial}{\partial x} (x + e^{4 y})

\frac{1}{2 x + e ^{4 y}}

Solution steps

\frac{\partial}{\partial x} (x + e^{4 y})

Treat

y

as a constant

Apply the chain rule:

\frac{1}{2 x + e ^{4 y}} \frac{\partial}{\partial x} (x + e^{4 y})

= \frac{1}{2 x + e ^{4 y}} \frac{\partial}{\partial x} (x + e^{4 y})

\frac{\partial}{\partial x} (x + e^{4 y}) = 1

= \frac{1}{2 x + e ^{4 y}} \cdot 1

Simplify

= \frac{1}{2 x + e ^{4 y}}

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- (x)^{2} 1

\frac{d}{d t} (- e^{3 t})

\int 6 x^{2} cos (x) d x

f (x) = x^{3} - 3 x + 2, at x = 2

What is (\partial)/(\partial x)(sqrt(x+e^{4y)}) ?
The answer to (\partial)/(\partial x)(sqrt(x+e^{4y)}) is 1/(2sqrt(x+e^{4y))}