What is the derivative of (12x^5+8x^3-2x^2/(4x^2)) ?

The derivative of (12x^5+8x^3-2x^2/(4x^2)) is 9x^2+2

What is the first derivative of (12x^5+8x^3-2x^2/(4x^2)) ?

The first derivative of (12x^5+8x^3-2x^2/(4x^2)) is 9x^2+2

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\frac{d}{d x} (\frac{12 x ^{5} + 8 x ^{3} - 2 x ^{2}}{4 x ^{2}})

9 x^{2} + 2

Solution steps

\frac{d}{d x} (\frac{12 x ^{5} + 8 x ^{3} - 2 x ^{2}}{4 x ^{2}})

Take the constant out:

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

= \frac{1}{4} \frac{d}{d x} (\frac{12 x ^{5} + 8 x ^{3} - 2 x ^{2}}{x ^{2}})

Apply the Quotient Rule:

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

= \frac{1}{4} \cdot \frac{\frac{d}{d x} ( 12 x ^{5} + 8 x ^{3} - 2 x ^{2} ) x ^{2} - \frac{d}{d x} ( x ^{2} ) ( 12 x ^{5} + 8 x ^{3} - 2 x ^{2} )}{( x ^{2} ) ^{2}}

\frac{d}{d x} (12 x^{5} + 8 x^{3} - 2 x^{2}) = 60 x^{4} + 24 x^{2} - 4 x

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

= \frac{1}{4} \cdot \frac{( 60 x ^{4} + 24 x ^{2} - 4 x ) x ^{2} - 2 x ( 12 x ^{5} + 8 x ^{3} - 2 x ^{2} )}{( x ^{2} ) ^{2}}

Simplify

\frac{1}{4} \cdot \frac{( 60 x ^{4} + 24 x ^{2} - 4 x ) x ^{2} - 2 x ( 12 x ^{5} + 8 x ^{3} - 2 x ^{2} )}{( x ^{2} ) ^{2}} : 9 x^{2} + 2

= 9 x^{2} + 2

\frac{8}{e ^{x} + e ^{- x}}

e^{- 6 x}, 0

\int x ln (5 x) d x

x \to 2 - lim (6 - 3 x - 3)

\int_{0}^{1} 2 x (8 - x^{2}) d x

What is the derivative of (12x^5+8x^3-2x^2/(4x^2)) ?
The derivative of (12x^5+8x^3-2x^2/(4x^2)) is 9x^2+2
What is the first derivative of (12x^5+8x^3-2x^2/(4x^2)) ?
The first derivative of (12x^5+8x^3-2x^2/(4x^2)) is 9x^2+2