What is the (xsin(2pix))^' ?

The (xsin(2pix))^' is sin(2pix)+2pixcos(2pix)

What is the first (xsin(2pix))^' ?

The first (xsin(2pix))^' is sin(2pix)+2pixcos(2pix)

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(x sin (2 π x))^{^{'}}

sin (2 π x) + 2 π x cos (2 π x)

Solution steps

(x sin (2 π x))^{'}

Apply the Product Rule:

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

f = x, g = sin (2 π x)

= x^{^{'}} sin (2 π x) + (sin (2 π x))^{^{'}} x

x^{'} = 1

(sin (2 π x))^{'} = cos (2 π x) \cdot 2 π

= 1 \cdot sin (2 π x) + cos (2 π x) \cdot 2 π x

Simplify

= sin (2 π x) + 2 π x cos (2 π x)

\int_{0}^{1} π (x - x^{4})^{2} d x

e^{t + 7}

\int 5 x 1 - x^{4} d x

x (x^{2} + 4)^{5}

f (x) = 5 x + 2 x^{2} + 7 e^{x}

What is the (xsin(2pix))^' ?
The (xsin(2pix))^' is sin(2pix)+2pixcos(2pix)
What is the first (xsin(2pix))^' ?
The first (xsin(2pix))^' is sin(2pix)+2pixcos(2pix)