What is the derivative of f(x)=5xsin(pix) ?

The derivative of f(x)=5xsin(pix) is 5(sin(pix)+pixcos(pix))

What is the first derivative of f(x)=5xsin(pix) ?

The first derivative of f(x)=5xsin(pix) is 5(sin(pix)+pixcos(pix))

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derivative of

f (x) = 5 x sin (π x)

5 (sin (π x) + π x cos (π x))

Solution steps

\frac{d}{d x} (5 x sin (π x))

Take the constant out:

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

= 5 \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)

= 5 (\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

= 5 (1 \cdot sin (π x) + cos (π x) π x)

Simplify

= 5 (sin (π x) + π x cos (π x))

What is the derivative of f(x)=5xsin(pix) ?
The derivative of f(x)=5xsin(pix) is 5(sin(pix)+pixcos(pix))
What is the first derivative of f(x)=5xsin(pix) ?
The first derivative of f(x)=5xsin(pix) is 5(sin(pix)+pixcos(pix))