en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of y=(1+4x)^{3/2}

Solution

derivative of

y = (1 + 4 x)^{\frac{3}{2}}

Solution

6 (4 x + 1)^{\frac{1}{2}}

Solution steps

\frac{d}{d x} ((1 + 4 x)^{\frac{3}{2}})

Apply the chain rule:

\frac{3 ( 1 + 4 x ) ^{\frac{1}{2}}}{2} \frac{d}{d x} (1 + 4 x)

= \frac{3 ( 1 + 4 x ) ^{\frac{1}{2}}}{2} \frac{d}{d x} (1 + 4 x)

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

= \frac{3 ( 1 + 4 x ) ^{\frac{1}{2}}}{2} \cdot 4

Simplify

\frac{3 ( 1 + 4 x ) ^{\frac{1}{2}}}{2} \cdot 4 : 6 (4 x + 1)^{\frac{1}{2}}

= 6 (4 x + 1)^{\frac{1}{2}}

Popular Examples

integral of xsin((npix)/3)

\int x sin (\frac{nπ x}{3}) d x

inverse oflaplace 1/(s^2(s^2+1^2))inverse laplace

\frac{1}{s ^{2} ( s ^{2} + 1 ^{2} )}

integral of x*arctan(x)

\int x \cdot arctan (x) d x

derivative of x(1-4/(x+3))derivative of

x (1 - \frac{4}{x + 3})

derivative of 2\sqrt[3]{x}-1 derivative of

Frequently Asked Questions (FAQ)

What is the derivative of y=(1+4x)^{3/2} ?
The derivative of y=(1+4x)^{3/2} is 6(4x+1)^{1/2}
What is the first derivative of y=(1+4x)^{3/2} ?
The first derivative of y=(1+4x)^{3/2} is 6(4x+1)^{1/2}