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Popular >

derivative of ln(4x^2+3x+3)

Solution

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

Solution

4 ln (2) x + 3

Solution steps

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

Simplify

ln (4) x^{2} + 3 x + 3 : 2 ln (2) x^{2} + 3 x + 3

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

Apply the Sum/Difference Rule:

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

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

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

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

\frac{d}{d x} (3) = 0

= 4 ln (2) x + 3 + 0

Simplify

= 4 ln (2) x + 3

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Frequently Asked Questions (FAQ)

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