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

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

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

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

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

Solution steps

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

Treat

y

as a constant

Apply the chain rule:

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

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

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

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

\frac{5}{1 + x ^{2}}

\frac{d}{d t} (\frac{sin ( t )}{1 + t ^{2}})

\int (2 x + 5) (x + 1)^{\frac{1}{2}} d x

e^{- 2 x} sin (x), 0

\int \frac{5 x ^{2} + 5 x + 3}{x ( x + 1 ) ^{2}} d x

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