What is the derivative of (5x^6+4x^5+3x^4/(6x^2)) ?

The derivative of (5x^6+4x^5+3x^4/(6x^2)) is (x(10x^2+6x+3))/3

What is the first derivative of (5x^6+4x^5+3x^4/(6x^2)) ?

The first derivative of (5x^6+4x^5+3x^4/(6x^2)) is (x(10x^2+6x+3))/3

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

\frac{d}{d x} (\frac{5 x ^{6} + 4 x ^{5} + 3 x ^{4}}{6 x ^{2}})

\frac{x ( 10 x ^{2} + 6 x + 3 )}{3}

Solution steps

\frac{d}{d x} (\frac{5 x ^{6} + 4 x ^{5} + 3 x ^{4}}{6 x ^{2}})

Take the constant out:

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

= \frac{1}{6} \frac{d}{d x} (\frac{5 x ^{6} + 4 x ^{5} + 3 x ^{4}}{x ^{2}})

Apply the Quotient Rule:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

= \frac{1}{6} \cdot \frac{\frac{d}{d x} ( 5 x ^{6} + 4 x ^{5} + 3 x ^{4} ) x ^{2} - \frac{d}{d x} ( x ^{2} ) ( 5 x ^{6} + 4 x ^{5} + 3 x ^{4} )}{( x ^{2} ) ^{2}}

\frac{d}{d x} (5 x^{6} + 4 x^{5} + 3 x^{4}) = 30 x^{5} + 20 x^{4} + 12 x^{3}

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

= \frac{1}{6} \cdot \frac{( 30 x ^{5} + 20 x ^{4} + 12 x ^{3} ) x ^{2} - 2 x ( 5 x ^{6} + 4 x ^{5} + 3 x ^{4} )}{( x ^{2} ) ^{2}}

Simplify

\frac{1}{6} \cdot \frac{( 30 x ^{5} + 20 x ^{4} + 12 x ^{3} ) x ^{2} - 2 x ( 5 x ^{6} + 4 x ^{5} + 3 x ^{4} )}{( x ^{2} ) ^{2}} : \frac{x ( 10 x ^{2} + 6 x + 3 )}{3}

= \frac{x ( 10 x ^{2} + 6 x + 3 )}{3}

\frac{x ^{2} - 2 e ^{x}}{x + 3 e ^{x}}

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

f (x) = sec^{2} (0)

\int \frac{1}{( 3 x - 1 ) ^{4}} d x

\frac{\partial}{\partial x} (- x^{2} y)

What is the derivative of (5x^6+4x^5+3x^4/(6x^2)) ?
The derivative of (5x^6+4x^5+3x^4/(6x^2)) is (x(10x^2+6x+3))/3
What is the first derivative of (5x^6+4x^5+3x^4/(6x^2)) ?
The first derivative of (5x^6+4x^5+3x^4/(6x^2)) is (x(10x^2+6x+3))/3