What is the derivative of 8ysin(x) ?

The derivative of 8ysin(x) is 8((dy)/(dx)sin(x)+cos(x)y)

What is the first derivative of 8ysin(x) ?

The first derivative of 8ysin(x) is 8((dy)/(dx)sin(x)+cos(x)y)

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\frac{d}{d x} (8 y sin (x))

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

Solution steps

\frac{d}{d x} (8 y sin (x))

Take the constant out:

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

= 8 \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)

= 8 (\frac{d y}{d x} sin (x) + \frac{d}{d x} (sin (x)) y)

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

= 8 (\frac{d y}{d x} sin (x) + cos (x) y)

cos (x), π

\int 8 x^{3} (2 x^{4} + 4) d x

\frac{d}{d x} (cos (x) - \frac{1}{2})

\int_{0}^{1} x e^{3 x} d x

\int 9 x (1 - x) d x

What is the derivative of 8ysin(x) ?
The derivative of 8ysin(x) is 8((dy)/(dx)sin(x)+cos(x)y)
What is the first derivative of 8ysin(x) ?
The first derivative of 8ysin(x) is 8((dy)/(dx)sin(x)+cos(x)y)