What is (\partial)/(\partial x)(ycos(2x)) ?

The answer to (\partial)/(\partial x)(ycos(2x)) is -2ysin(2x)

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(\partial)/(\partial x)(ycos(2x))

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

- 2 y sin (2 x)

Solution steps

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

Treat

y

as a constant

Take the constant out:

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

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

Apply the chain rule:

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

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

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

= y (- sin (2 x) \cdot 2)

Simplify

= - 2 y sin (2 x)

d er i v a t i v e \frac{x - 9 x x}{x}

y (2 x + x^{2} cot (x)) d x + x^{2} (1 + y) d y = 0

d er i v a t i v e e^{3 x}

e x p an d (2 x^{2} + 5) (4 x - 1)

\int \frac{5 - 50 x}{81 - 25 x ^{2}} d x

What is (\partial)/(\partial x)(ycos(2x)) ?
The answer to (\partial)/(\partial x)(ycos(2x)) is -2ysin(2x)