What is (\partial)/(\partial x)(5sin(2x)cos(5y)) ?

The answer to (\partial)/(\partial x)(5sin(2x)cos(5y)) is 10cos(2x)cos(5y)

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(\partial)/(\partial x)(5sin(2x)cos(5y))

\frac{\partial}{\partial x} (5 sin (2 x) cos (5 y))

10 cos (2 x) cos (5 y)

Solution steps

\frac{\partial}{\partial x} (5 sin (2 x) cos (5 y))

Treat

y

as a constant

Take the constant out:

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

= 5 cos (5 y) \frac{\partial}{\partial x} (sin (2 x))

Apply the chain rule:

cos (2 x) \frac{\partial}{\partial x} (2 x)

= cos (2 x) \frac{\partial}{\partial x} (2 x)

\frac{\partial}{\partial x} (2 x) = 2

= 5 cos (5 y) cos (2 x) \cdot 2

Simplify

= 10 cos (2 x) cos (5 y)

\int_{0}^{3} 3 x + 16 d x

y = ln ∣ sin (x) ∣

\frac{d}{d x} ((x^{2 - x})^{5} (x - 3 x^{2}))

\int \frac{81}{x ^{3} - 9 x ^{2}} d x

\frac{x ^{2} + 1}{x ^{2} + x + 1}

What is (\partial)/(\partial x)(5sin(2x)cos(5y)) ?
The answer to (\partial)/(\partial x)(5sin(2x)cos(5y)) is 10cos(2x)cos(5y)