What is (\partial)/(\partial x)(5sin(2(5x+6y))) ?

The answer to (\partial)/(\partial x)(5sin(2(5x+6y))) is 50cos(2(5x+6y))

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(\partial)/(\partial x)(5sin(2(5x+6y)))

\frac{\partial}{\partial x} (5 sin (2 (5 x + 6 y)))

50 cos (2 (5 x + 6 y))

Solution steps

\frac{\partial}{\partial x} (5 sin (2 (5 x + 6 y)))

Treat

y

as a constant

Take the constant out:

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

= 5 \frac{\partial}{\partial x} (sin (2 (5 x + 6 y)))

Apply the chain rule:

cos (2 (5 x + 6 y)) \frac{\partial}{\partial x} (2 (5 x + 6 y))

= cos (2 (5 x + 6 y)) \frac{\partial}{\partial x} (2 (5 x + 6 y))

\frac{\partial}{\partial x} (2 (5 x + 6 y)) = 10

= 5 cos (2 (5 x + 6 y)) \cdot 10

Simplify

= 50 cos (2 (5 x + 6 y))

\int x^{2} \cdot x^{3} + 1 d x

x \to 2 lim (\frac{x ^{3} - 1}{x - 1})

\frac{d}{d x} (1 + ln (x))

n \to \infty lim (r^{n})

x \to 0 lim (x^{4} cos (\frac{8}{x}))

What is (\partial)/(\partial x)(5sin(2(5x+6y))) ?
The answer to (\partial)/(\partial x)(5sin(2(5x+6y))) is 50cos(2(5x+6y))