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

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

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

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

- sin (2 x)

Solution steps

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

Take the constant out:

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

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

Apply the chain rule:

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

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

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

= - 2 sin (x) cos (x)

Use the Double Angle identity:

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

= - sin (2 x)

\frac{d}{d x} (arcsin (f (x)))

\int tan (4 x) (sec (4 x))^{2} d x

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

δ (t - 1)

\int_{0}^{π} cos (x + π) d x

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