What is the derivative of ycos(x) ?

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

What is the first derivative of ycos(x) ?

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

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

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

Solution steps

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

Apply the Product Rule:

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

f = y, g = cos (x)

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

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

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

Simplify

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

cos (3 x^{2} + 4) \cdot 6 x

\int \frac{1}{3 x ^{2} + 6 x + 6} d x

sin (x), x = 0, y = 0, x = \frac{π}{6}

y^{^{''}} + 4 y^{^{'}} + 4 y = x \cdot cos (2 x) + 3 e^{- 2 x}

\frac{d x}{d t} + 3 x = e^{- 2 t}

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