What is the derivative of y=8xsin(x) ?

The derivative of y=8xsin(x) is 8(sin(x)+xcos(x))

What is the first derivative of y=8xsin(x) ?

The first derivative of y=8xsin(x) is 8(sin(x)+xcos(x))

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derivative of

y = 8 x sin (x)

8 (sin (x) + x cos (x))

Solution steps

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

Take the constant out:

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

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

Apply the Product Rule:

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

f = x, g = sin (x)

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

\frac{d x}{d x} = 1

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

= 8 (1 \cdot sin (x) + cos (x) x)

Simplify

= 8 (sin (x) + x cos (x))

x \to 0 lim (\frac{sin ( 3 ) ( x )}{x})

\int x x^{4} - 9 d x

\int_{0}^{3} (x^{2} - 2 x) d x

y^{^{''}} + 11 y^{^{'}} - 28 y = 0

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

What is the derivative of y=8xsin(x) ?
The derivative of y=8xsin(x) is 8(sin(x)+xcos(x))
What is the first derivative of y=8xsin(x) ?
The first derivative of y=8xsin(x) is 8(sin(x)+xcos(x))