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

The derivative of f(x)=8xsin(pix) is 8(sin(pix)+pixcos(pix))

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

The first derivative of f(x)=8xsin(pix) is 8(sin(pix)+pixcos(pix))

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derivative of

f (x) = 8 x sin (π x)

8 (sin (π x) + π x cos (π x))

Solution steps

\frac{d}{d x} (8 x sin (π x))

Take the constant out:

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

= 8 \frac{d}{d x} (x sin (π x))

Apply the Product Rule:

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

f = x, g = sin (π x)

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

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

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

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

Simplify

= 8 (sin (π x) + π x cos (π x))

4 t^{- \frac{1}{8}} + 4 ln (t) + ln (5)

\int (x^{2} + 3 x + 2) e^{x} d x

x \to 3 lim (4 x^{2} - \frac{1}{x})

\int \frac{2 x ^{3} + 7 x ^{2} + 2 x + 9}{2 x + 3} d x

x e^{- x^{10}}

What is the derivative of f(x)=8xsin(pix) ?
The derivative of f(x)=8xsin(pix) is 8(sin(pix)+pixcos(pix))
What is the first derivative of f(x)=8xsin(pix) ?
The first derivative of f(x)=8xsin(pix) is 8(sin(pix)+pixcos(pix))