What is the derivative of-3ln(3+4x^2+5x^3-9) ?

The derivative of-3ln(3+4x^2+5x^3-9) is 15x^2-(24x)/(4x^2+3)

What is the first derivative of-3ln(3+4x^2+5x^3-9) ?

The first derivative of-3ln(3+4x^2+5x^3-9) is 15x^2-(24x)/(4x^2+3)

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\frac{d}{d x} (- 3 ln (3 + 4 x^{2}) + 5 x^{3} - 9)

15 x^{2} - \frac{24 x}{4 x ^{2} + 3}

Solution steps

\frac{d}{d x} (- 3 ln (3 + 4 x^{2}) + 5 x^{3} - 9)

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= - \frac{d}{d x} (3 ln (3 + 4 x^{2})) + \frac{d}{d x} (5 x^{3}) - \frac{d}{d x} (9)

\frac{d}{d x} (3 ln (3 + 4 x^{2})) = \frac{24 x}{3 + 4 x ^{2}}

\frac{d}{d x} (5 x^{3}) = 15 x^{2}

\frac{d}{d x} (9) = 0

= - \frac{24 x}{3 + 4 x ^{2}} + 15 x^{2} - 0

Simplify

= 15 x^{2} - \frac{24 x}{4 x ^{2} + 3}

What is the derivative of-3ln(3+4x^2+5x^3-9) ?
The derivative of-3ln(3+4x^2+5x^3-9) is 15x^2-(24x)/(4x^2+3)
What is the first derivative of-3ln(3+4x^2+5x^3-9) ?
The first derivative of-3ln(3+4x^2+5x^3-9) is 15x^2-(24x)/(4x^2+3)