What is the derivative of e^{4xy} ?

The derivative of e^{4xy} is e^{4xy}*4(y+x(dy)/(dx))

What is the first derivative of e^{4xy} ?

The first derivative of e^{4xy} is e^{4xy}*4(y+x(dy)/(dx))

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\frac{d}{d x} (e^{4 x y})

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

Solution steps

\frac{d}{d x} (e^{4 x y})

Apply the chain rule:

e^{4 x y} \frac{d}{d x} (4 x y)

= e^{4 x y} \frac{d}{d x} (4 x y)

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

= e^{4 x y} \cdot 4 (y + x \frac{d y}{d x})

\int cos^{3} (5 x) sin^{- 2} (5 x) d x

\int 2 e^{- 3 x} d x

x \to 0 lim (cos^{\frac{1}{x}} (x))

sin^{2} (y) d x + cos^{2} (x) d y = 0

x \to - 5 lim (2 x + 3)

What is the derivative of e^{4xy} ?
The derivative of e^{4xy} is e^{4xy}*4(y+x(dy)/(dx))
What is the first derivative of e^{4xy} ?
The first derivative of e^{4xy} is e^{4xy}*4(y+x(dy)/(dx))