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

The derivative of ((x^4-5))/((x^2+3)) is (2x^5+12x^3+10x)/((x^2+3)^2)

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

The first derivative of ((x^4-5))/((x^2+3)) is (2x^5+12x^3+10x)/((x^2+3)^2)

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derivative of

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

\frac{2 x ^{5} + 12 x ^{3} + 10 x}{( x ^{2} + 3 ) ^{2}}

Solution steps

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

Apply the Quotient Rule:

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

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

\frac{d}{d x} (x^{4} - 5) = 4 x^{3}

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

= \frac{4 x ^{3} ( x ^{2} + 3 ) - 2 x ( x ^{4} - 5 )}{( x ^{2} + 3 ) ^{2}}

Expand

4 x^{3} (x^{2} + 3) - 2 x (x^{4} - 5) : 2 x^{5} + 12 x^{3} + 10 x

= \frac{2 x ^{5} + 12 x ^{3} + 10 x}{( x ^{2} + 3 ) ^{2}}

d er i v a t i v e 3 + 4 t

d er i v a t i v e \frac{x}{x ^{3} + 1}

d er i v a t i v e a^{3} - 3

d er i v a t i v e y = \frac{( x ^{2} + 1 )}{x ^{3}}

d er i v a t i v e t^{2} + 1

What is the derivative of ((x^4-5))/((x^2+3)) ?
The derivative of ((x^4-5))/((x^2+3)) is (2x^5+12x^3+10x)/((x^2+3)^2)
What is the first derivative of ((x^4-5))/((x^2+3)) ?
The first derivative of ((x^4-5))/((x^2+3)) is (2x^5+12x^3+10x)/((x^2+3)^2)