What is (\partial)/(\partial x)(e^{x^2-y^2+4y}) ?

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

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(\partial)/(\partial x)(e^{x^2-y^2+4y})

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

e^{x^{2} - y^{2} + 4 y} \cdot 2 x

Solution steps

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

Treat

y

as a constant

Apply the chain rule:

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

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

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

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

\int_{1}^{4} (x^{2} - 2) d x

f (x) = 3 sin (3 x)

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

\frac{d}{d x} (3 x^{5} - 30 x^{3})

f (x) = 5 x^{2} - 3 x + 7

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