What is the derivative of (x^3+1/(x^2+3)) ?

The derivative of (x^3+1/(x^2+3)) is (x^4+9x^2-2x)/((x^2+3)^2)

What is the first derivative of (x^3+1/(x^2+3)) ?

The first derivative of (x^3+1/(x^2+3)) is (x^4+9x^2-2x)/((x^2+3)^2)

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\frac{d}{d x} (\frac{x ^{3} + 1}{x ^{2} + 3})

\frac{x ^{4} + 9 x ^{2} - 2 x}{( x ^{2} + 3 ) ^{2}}

Solution steps

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

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

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

= \frac{3 x ^{2} ( x ^{2} + 3 ) - 2 x ( x ^{3} + 1 )}{( x ^{2} + 3 ) ^{2}}

Expand

3 x^{2} (x^{2} + 3) - 2 x (x^{3} + 1) : x^{4} + 9 x^{2} - 2 x

= \frac{x ^{4} + 9 x ^{2} - 2 x}{( x ^{2} + 3 ) ^{2}}

(sin (x) + 2 tan (x)) (sec (x) - 3 csc (x))

\frac{d}{d x} (\frac{1}{x ^{12}})

tan (2 x^{2} - x + 3)

y = 9 sec (\frac{1}{3} x)

f (x) = 2 x ln (x) + x

What is the derivative of (x^3+1/(x^2+3)) ?
The derivative of (x^3+1/(x^2+3)) is (x^4+9x^2-2x)/((x^2+3)^2)
What is the first derivative of (x^3+1/(x^2+3)) ?
The first derivative of (x^3+1/(x^2+3)) is (x^4+9x^2-2x)/((x^2+3)^2)