What is the derivative of (x^4)/(4+x^{33)+x^{22}} ?

The derivative of (x^4)/(4+x^{33)+x^{22}} is (-29x^{36}-18x^{25}+16x^3)/((4+x^{33)+x^{22})^2}

What is the first derivative of (x^4)/(4+x^{33)+x^{22}} ?

The first derivative of (x^4)/(4+x^{33)+x^{22}} is (-29x^{36}-18x^{25}+16x^3)/((4+x^{33)+x^{22})^2}

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derivative of

\frac{x ^{4}}{4 + x ^{33} + x ^{22}}

\frac{- 29 x ^{36} - 18 x ^{25} + 16 x ^{3}}{( 4 + x ^{33} + x ^{22} ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{x ^{4}}{4 + x ^{33} + x ^{22}})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( x ^{4} ) ( 4 + x ^{33} + x ^{22} ) - \frac{d}{d x} ( 4 + x ^{33} + x ^{22} ) x ^{4}}{( 4 + x ^{33} + x ^{22} ) ^{2}}

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

\frac{d}{d x} (4 + x^{33} + x^{22}) = 33 x^{32} + 22 x^{21}

= \frac{4 x ^{3} ( 4 + x ^{33} + x ^{22} ) - ( 33 x ^{32} + 22 x ^{21} ) x ^{4}}{( 4 + x ^{33} + x ^{22} ) ^{2}}

Expand

4 x^{3} (4 + x^{33} + x^{22}) - (33 x^{32} + 22 x^{21}) x^{4} : - 29 x^{36} - 18 x^{25} + 16 x^{3}

= \frac{- 29 x ^{36} - 18 x ^{25} + 16 x ^{3}}{( 4 + x ^{33} + x ^{22} ) ^{2}}

\frac{64}{x ^{3}}

f (x) = x^{3} + 1

\frac{8 x}{3}

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

y = x^{3} + 4 x^{2} + 5 x + 7

What is the derivative of (x^4)/(4+x^{33)+x^{22}} ?
The derivative of (x^4)/(4+x^{33)+x^{22}} is (-29x^{36}-18x^{25}+16x^3)/((4+x^{33)+x^{22})^2}
What is the first derivative of (x^4)/(4+x^{33)+x^{22}} ?
The first derivative of (x^4)/(4+x^{33)+x^{22}} is (-29x^{36}-18x^{25}+16x^3)/((4+x^{33)+x^{22})^2}