What is (\partial)/(\partial x)(sin^2(2x+3y)) ?

The answer to (\partial)/(\partial x)(sin^2(2x+3y)) is 4sin(2x+3y)cos(2x+3y)

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(\partial)/(\partial x)(sin^2(2x+3y))

\frac{\partial}{\partial x} (sin^{2} (2 x + 3 y))

4 sin (2 x + 3 y) cos (2 x + 3 y)

Solution steps

\frac{\partial}{\partial x} (sin^{2} (2 x + 3 y))

Treat

y

as a constant

Apply the chain rule:

2 sin (2 x + 3 y) \frac{\partial}{\partial x} (sin (2 x + 3 y))

= 2 sin (2 x + 3 y) \frac{\partial}{\partial x} (sin (2 x + 3 y))

\frac{\partial}{\partial x} (sin (2 x + 3 y)) = cos (2 x + 3 y) \cdot 2

= 2 sin (2 x + 3 y) cos (2 x + 3 y) \cdot 2

Simplify

= 4 sin (2 x + 3 y) cos (2 x + 3 y)

\int_{0}^{1} x^{2} (x^{3} - 2)^{3} d x

\frac{\partial}{\partial x} (\frac{t}{x})

\frac{d y}{d x} + (\frac{3}{x}) y = - 4 x - 10

\int \frac{1}{x ^{2} - 4} d x

\frac{d y}{d x} = \frac{2}{x}

What is (\partial)/(\partial x)(sin^2(2x+3y)) ?
The answer to (\partial)/(\partial x)(sin^2(2x+3y)) is 4sin(2x+3y)cos(2x+3y)