What is the derivative of ysin(x) ?

The derivative of ysin(x) is (dy)/(dx)sin(x)+cos(x)y

What is the first derivative of ysin(x) ?

The first derivative of ysin(x) is (dy)/(dx)sin(x)+cos(x)y

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

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

Solution steps

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

Apply the Product Rule:

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

f = y, g = sin (x)

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

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

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

\int \frac{x ^{8} - 5 x}{x ^{6}} d x

\int 7 cos^{4} (x) d x

\frac{d y}{d t} + e^{t} y = 20 e^{t}

\frac{\partial}{\partial z} (3 x z)

\frac{1}{s ( s ^{2} + 3 s + 2 )}

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