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

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

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

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

cos (5 x + 2 y) \cdot 5

Solution steps

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

Treat

y

as a constant

Apply the chain rule:

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

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

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

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

\int e^{t} + 2 t + ln (t) d t

\int \frac{1}{x ^{2} + 2 x - 8} d x

\frac{d}{d x} (- sin (2 x) \cdot 2)

\int \frac{1}{x ^{2} \cdot 5 + x ^{2}} d x

y^{^{''}} - 8 y^{^{'}} + 18 y = 0, y (0) = - 4, y^{^{'}} (0) = 3

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