What is the (x*sin(x))^' ?

The (x*sin(x))^' is sin(x)+xcos(x)

What is the first (x*sin(x))^' ?

The first (x*sin(x))^' is sin(x)+xcos(x)

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(x \cdot sin (x))^{^{'}}

sin (x) + x cos (x)

Solution steps

(x sin (x))^{'}

Apply the Product Rule:

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

f = x, g = sin (x)

= x^{^{'}} sin (x) + (sin (x))^{^{'}} x

x^{'} = 1

(sin (x))^{'} = cos (x)

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

Simplify

= sin (x) + x cos (x)

\frac{d}{d x} (4 - x^{2} - y^{2})

d er i v a t i v e f (x) = sin (x) + \frac{1}{2} cot (x)

\int_{- 2}^{0} (2 + 4 - x^{2}) d x

\int \frac{4 x - 11}{2 x ^{2} + 7 x - 4} d x

\frac{d}{d x} (\frac{x ^{3} + x ^{2} - x + 2}{x + 2})