en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of (e^{4x^2+1}/8)

Solution

\frac{d}{d x} (\frac{e ^{4 x^{2} + 1}}{8})

Solution

e^{4 x^{2} + 1} x

Solution steps

\frac{d}{d x} (\frac{e ^{4 x^{2} + 1}}{8})

Take the constant out:

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

= \frac{1}{8} \frac{d}{d x} (e^{4 x^{2} + 1})

Apply the chain rule:

e^{4 x^{2} + 1} \frac{d}{d x} (4 x^{2} + 1)

= e^{4 x^{2} + 1} \frac{d}{d x} (4 x^{2} + 1)

\frac{d}{d x} (4 x^{2} + 1) = 8 x

= \frac{1}{8} e^{4 x^{2} + 1} \cdot 8 x

Simplify

\frac{1}{8} e^{4 x^{2} + 1} \cdot 8 x : e^{4 x^{2} + 1} x

= e^{4 x^{2} + 1} x

Popular Examples

derivative of-2xsin(2x)

\frac{d}{d x} (- 2 x sin (2 x))

integral from 0 to pi/3 of sec^3(x)

\int_{0}^{\frac{π}{3}} sec^{3} (x) d x

integral of (x+1)/(sqrt(4-x^2))

\int \frac{x + 1}{4 - x ^{2}} d x

derivative of 5x(sin(x+cos(x)))

\frac{d}{d x} (5 x (sin (x) + cos (x)))

7 x^{2} y + y^{^{'}} = 6 x^{2}

Frequently Asked Questions (FAQ)

What is the derivative of (e^{4x^2+1}/8) ?
The derivative of (e^{4x^2+1}/8) is e^{4x^2+1}x
What is the first derivative of (e^{4x^2+1}/8) ?
The first derivative of (e^{4x^2+1}/8) is e^{4x^2+1}x