What is (\partial)/(\partial x)(e^{(y+1)x}) ?

The answer to (\partial)/(\partial x)(e^{(y+1)x}) is e^{(y+1)x}(y+1)

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(\partial)/(\partial x)(e^{(y+1)x})

\frac{\partial}{\partial x} (e^{(y + 1) x})

e^{(y + 1) x} (y + 1)

Solution steps

\frac{\partial}{\partial x} (e^{(y + 1) x})

Treat

y

as a constant

Apply the chain rule:

e^{(y + 1) x} \frac{\partial}{\partial x} ((y + 1) x)

= e^{(y + 1) x} \frac{\partial}{\partial x} ((y + 1) x)

\frac{\partial}{\partial x} ((y + 1) x) = y + 1

= e^{(y + 1) x} (y + 1)

f (x) = \frac{x ^{3} + 9 x ^{2} + x - 8}{x}

\frac{\partial}{\partial x} (4 a x)

\frac{d}{d x} ((x^{2} + 6)^{9})

\frac{d}{d x} (cosh (4 x))

\int \frac{2 x ^{2} + 7 x - 8}{x - 7} d x

What is (\partial)/(\partial x)(e^{(y+1)x}) ?
The answer to (\partial)/(\partial x)(e^{(y+1)x}) is e^{(y+1)x}(y+1)