What is the derivative of ycos(2x) ?

The derivative of ycos(2x) is cos(2x)(dy)/(dx)-2sin(2x)y

What is the first derivative of ycos(2x) ?

The first derivative of ycos(2x) is cos(2x)(dy)/(dx)-2sin(2x)y

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

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

Solution steps

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

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = y, g = cos (2 x)

= \frac{d y}{d x} cos (2 x) + \frac{d}{d x} (cos (2 x)) y

\frac{d}{d x} (cos (2 x)) = - sin (2 x) \cdot 2

= \frac{d y}{d x} cos (2 x) + (- sin (2 x) \cdot 2) y

Simplify

= cos (2 x) \frac{d y}{d x} - 2 sin (2 x) y

f (x) = x^{3} - 3 x + 2

\int \frac{4}{16 x ^{2} + 1} d x

\int 2 e^{2 t + 5} d t

\frac{d}{d x} ((ln (3) + e^{x^{e}})^{e})

y^{^{''}} + y^{^{'}} - 2 y = 9 e^{t} - 6 t

What is the derivative of ycos(2x) ?
The derivative of ycos(2x) is cos(2x)(dy)/(dx)-2sin(2x)y
What is the first derivative of ycos(2x) ?
The first derivative of ycos(2x) is cos(2x)(dy)/(dx)-2sin(2x)y