What is (\partial)/(\partial y)(e^{7xe^y}) ?

The answer to (\partial)/(\partial y)(e^{7xe^y}) is 7e^{7e^yx+y}x

Popular >

(\partial)/(\partial y)(e^{7xe^y})

\frac{\partial}{\partial y} (e^{7 x e^{y}})

7 e^{7 e^{y} x + y} x

Solution steps

\frac{\partial}{\partial y} (e^{7 x e^{y}})

Treat

x

as a constant

Apply the chain rule:

e^{7 x e^{y}} \frac{\partial}{\partial y} (7 x e^{y})

= e^{7 x e^{y}} \frac{\partial}{\partial y} (7 x e^{y})

\frac{\partial}{\partial y} (7 x e^{y}) = 7 x e^{y}

= e^{7 x e^{y}} \cdot 7 x e^{y}

Apply exponent rule:

a^{b} \cdot a^{c} = a^{b + c}

e^{7 x e^{y}} e^{y} = e^{7 e^{y} x + y}

= 7 e^{7 e^{y} x + y} x

f (x) = 6 x^{3} cot (x)

f (x) = x^{3} 5 - x^{2}, at x = 2

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

\frac{\partial}{\partial x} (x^{3} + sin (3 y))

\int \frac{1}{x ^{2} + c} d x

What is (\partial)/(\partial y)(e^{7xe^y}) ?
The answer to (\partial)/(\partial y)(e^{7xe^y}) is 7e^{7e^yx+y}x