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

The answer to (\partial)/(\partial x)(sin^2(x-5y)) is sin(2(x-5y))

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(\partial)/(\partial x)(sin^2(x-5y))

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

sin (2 (x - 5 y))

Solution steps

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

Treat

y

as a constant

Apply the chain rule:

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

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

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

= 2 sin (x - 5 y) cos (x - 5 y)

Use the Double Angle identity:

2 sin (x) cos (x) = sin (2 x)

= sin (2 (x - 5 y))

\frac{d}{d h} (\frac{π h ^{2}}{3} (36 - h))

x^{3} y^{^{'}} + 2 x^{2} y = - 2 cos (3 x) y^{- \frac{1}{2}}

\int \frac{sin ( x )}{1 - 2 cos ( x )} d x

\int e^{x} cos (9 x) d x

\frac{\partial}{\partial x} (5 x^{4} + y^{8})

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