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

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

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

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

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

Solution steps

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

Treat

y

as a constant

Take the constant out:

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

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

\frac{x ( - 4 x ^{2} + 1 + 1 )}{4}

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

x \to - \frac{π}{2} lim (- tan (0.5 x))

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

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

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