en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of (x-2^3(4x-7)^6)

Solution

\frac{d}{d x} ((x - 2)^{3} (4 x - 7)^{6})

Solution

3 (x - 2)^{2} (4 x - 7)^{6} + 24 (4 x - 7)^{5} (x - 2)^{3}

Solution steps

\frac{d}{d x} ((x - 2)^{3} (4 x - 7)^{6})

Apply the Product Rule:

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

f = (x - 2)^{3}, g = (4 x - 7)^{6}

= \frac{d}{d x} ((x - 2)^{3}) (4 x - 7)^{6} + \frac{d}{d x} ((4 x - 7)^{6}) (x - 2)^{3}

\frac{d}{d x} ((x - 2)^{3}) = 3 (x - 2)^{2}

\frac{d}{d x} ((4 x - 7)^{6}) = 24 (4 x - 7)^{5}

= 3 (x - 2)^{2} (4 x - 7)^{6} + 24 (4 x - 7)^{5} (x - 2)^{3}

Popular Examples

integral of (cos(8x))/(1-cos(8x))

\int \frac{cos ( 8 x )}{1 - cos ( 8 x )} d x

integral of 0.03e^{0.05x}

\int 0.03 e^{0.05 x} d x

derivative of f(x)=(9(5^x))/(x^5)derivative of

f (x) = \frac{9 ( 5 ^{x} )}{x ^{5}}

integral of log_{x}(x)

\int lo g_{x} (x) d x

integral of (5x^2-3)/(x(x^2-1))

\int \frac{5 x ^{2} - 3}{x ( x ^{2} - 1 )} d x

Frequently Asked Questions (FAQ)

What is the derivative of (x-2^3(4x-7)^6) ?
The derivative of (x-2^3(4x-7)^6) is 3(x-2)^2(4x-7)^6+24(4x-7)^5(x-2)^3
What is the first derivative of (x-2^3(4x-7)^6) ?
The first derivative of (x-2^3(4x-7)^6) is 3(x-2)^2(4x-7)^6+24(4x-7)^5(x-2)^3