What is the derivative of 8x*sin(x) ?

The derivative of 8x*sin(x) is 8(sin(x)+xcos(x))

What is the first derivative of 8x*sin(x) ?

The first derivative of 8x*sin(x) is 8(sin(x)+xcos(x))

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

\int \frac{1}{π} sin (π x) d x

y = 4 x

y = \frac{x}{8 + x}

\frac{d}{d x} (cot^{7} (x))

2 y y^{^{'}} + 2 = y^{2} + 2 x, y (0) = 4

What is the derivative of 8x*sin(x) ?
The derivative of 8x*sin(x) is 8(sin(x)+xcos(x))
What is the first derivative of 8x*sin(x) ?
The first derivative of 8x*sin(x) is 8(sin(x)+xcos(x))