en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of 8xsin(pix)

Solution

\frac{d}{d x} (8 x sin (π x))

Solution

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))

Popular Examples

\frac{d}{d y} (y^{4})

integral of (3x^3+2)/(x^2sqrt(x^2-4))

\int \frac{3 x ^{3} + 2}{x ^{2} x ^{2} - 4} d x

(d^3)/(dx^3)(3/x)

\frac{d ^{3}}{d x ^{3}} (\frac{3}{x})

integral of sin(2x+5)

\int sin (2 x + 5) d x

derivative of f(x)=arctan((x-1)/(x+1))derivative of

f (x) = arctan (\frac{x - 1}{x + 1})

Frequently Asked Questions (FAQ)

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