What is (\partial)/(\partial x)(e^{5x}cos(7y)) ?

The answer to (\partial)/(\partial x)(e^{5x}cos(7y)) is cos(7y)e^{5x}*5

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(\partial)/(\partial x)(e^{5x}cos(7y))

\frac{\partial}{\partial x} (e^{5 x} cos (7 y))

cos (7 y) e^{5 x} \cdot 5

Solution steps

\frac{\partial}{\partial x} (e^{5 x} cos (7 y))

Treat

y

as a constant

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= cos (7 y) \frac{\partial}{\partial x} (e^{5 x})

Apply the chain rule:

e^{5 x} \frac{\partial}{\partial x} (5 x)

= e^{5 x} \frac{\partial}{\partial x} (5 x)

\frac{\partial}{\partial x} (5 x) = 5

= cos (7 y) e^{5 x} \cdot 5

\frac{d}{d x} (\frac{2 x + 3}{5 x + 4})

\frac{d}{d x} (2 e^{(x - 5)})

\int \frac{( x ^{2} + 2 )}{x + 1} d x

\frac{d}{d x} ((2 x^{2} - 3)^{3})

y = \frac{2}{( 4 x - 3 ) ^{\frac{1}{2}}}

What is (\partial)/(\partial x)(e^{5x}cos(7y)) ?
The answer to (\partial)/(\partial x)(e^{5x}cos(7y)) is cos(7y)e^{5x}*5