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

The derivative of e^{3xy} is e^{3xy}*3(y+x(dy)/(dx))

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

The first derivative of e^{3xy} is e^{3xy}*3(y+x(dy)/(dx))

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

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

Solution steps

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

Apply the chain rule:

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

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

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

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

h \to 0 lim (\frac{( f ( h ) ( 4 + h ) - f ( 4 ) )}{h})

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

y = x^{3}

x y^{^{'}} + x y = 1 - y

(2 x y^{2} - 3 y^{3}) d x + (7 - 3 x y^{2}) d y = 0

What is the derivative of e^{3xy} ?
The derivative of e^{3xy} is e^{3xy}*3(y+x(dy)/(dx))
What is the first derivative of e^{3xy} ?
The first derivative of e^{3xy} is e^{3xy}*3(y+x(dy)/(dx))