What is the (xsin(x))^' ?

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

What is the first (xsin(x))^' ?

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

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(x 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{9}{s ^{2} + 9 s + 9}

(e^{- ∣ x ∣})^{^{'}}

\int sin (x^{- 1}) d x

\int \frac{e ^{x}}{9 + e ^{x}} d x

\int \frac{5 x + 5}{x ^{2} + 1} d x