What is the derivative of e^{2x^2+3xy} ?

The derivative of e^{2x^2+3xy} is e^{2x^2+3xy}(4x+3y)

What is the first derivative of e^{2x^2+3xy} ?

The first derivative of e^{2x^2+3xy} is e^{2x^2+3xy}(4x+3y)

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derivative of

e^{2 x^{2} + 3 x y}

e^{2 x^{2} + 3 x y} (4 x + 3 y)

Solution steps

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

Treat

y

as a constant

Apply the chain rule:

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

= e^{2 x^{2} + 3 x y} \frac{d}{d x} (2 x^{2} + 3 x y)

\frac{d}{d x} (2 x^{2} + 3 x y) = 4 x + 3 y

= e^{2 x^{2} + 3 x y} (4 x + 3 y)

sec^{2} (2 x + 1)

\frac{2}{3} \frac{x ^{4}}{6} + 5 \frac{x ^{4}}{5}

e^{l} o gx + 1

y = (2 t - 3)^{2}

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

What is the derivative of e^{2x^2+3xy} ?
The derivative of e^{2x^2+3xy} is e^{2x^2+3xy}(4x+3y)
What is the first derivative of e^{2x^2+3xy} ?
The first derivative of e^{2x^2+3xy} is e^{2x^2+3xy}(4x+3y)