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

The answer to (\partial)/(\partial x)(e^{2x^3-3y}) is e^{2x^3-3y}*6x^2

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

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

e^{2 x^{3} - 3 y} \cdot 6 x^{2}

Solution steps

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

Treat

y

as a constant

Apply the chain rule:

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

= e^{2 x^{3} - 3 y} \frac{\partial}{\partial x} (2 x^{3} - 3 y)

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

= e^{2 x^{3} - 3 y} \cdot 6 x^{2}

\int \frac{x ^{2} - 8 x - 1}{( x - 1 ) ^{2} ( x ^{2} + 1 )} d x

\frac{d}{d x} (2 x + 8)

\frac{d}{d x} ([arctan (3 x)]^{2})

1680 (2 x + 5)^{4}

y^{^{''}} + y = 5 e^{- 8 x}

What is (\partial)/(\partial x)(e^{2x^3-3y}) ?
The answer to (\partial)/(\partial x)(e^{2x^3-3y}) is e^{2x^3-3y}*6x^2