What is the derivative of $f (x) = 3 x^{2} ln 2 x$ $f(x) = 3x^2 ln 2x$ ?

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What is the derivative of $f (x) = 3 x^{2} ln 2 x$ $f(x) = 3x^2 ln 2x$ ?

1 Answer

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Answer 1 · 2017-11-04T15:53:31

$\frac{d}{d x} (3 x^{2} ln 2 x) = 3 x (1 + 2 ln 2 x)$ $d/dx ( 3x^2ln2x) = 3x( 1+ 2ln 2x )$

Explanation:

Using the product rule:

$\frac{d}{d x} (3 x^{2} ln 2 x) = \frac{d}{d x} (3 x^{2}) ln 2 x + 3 x^{2} \frac{d}{d x} (ln 2 x)$ $d/dx ( 3x^2ln2x) = d/dx(3x^2)ln 2x + 3x^2 d/dx (ln2x)$

$\frac{d}{d x} (3 x^{2} ln 2 x) = 6 x ln 2 x + 3 x^{2} \frac{2}{2 x}$ $d/dx ( 3x^2ln2x) = 6xln 2x + 3x^2 2/(2x)$

$\frac{d}{d x} (3 x^{2} ln 2 x) = 6 x ln 2 x + 3 x$ $d/dx ( 3x^2ln2x) = 6xln 2x + 3x$

$\frac{d}{d x} (3 x^{2} ln 2 x) = 3 x (1 + 2 ln 2 x)$ $d/dx ( 3x^2ln2x) = 3x( 1+ 2ln 2x )$

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What is the derivative of $f (x) = 3 x^{2} ln 2 x$ $f(x) = 3x^2 ln 2x$ ?

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Explanation:

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What is the derivative of f(x) = 3x^2 ln 2xf(x)=3x2ln2x f(x) = 3x^2 ln 2x?

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What is the derivative of $f (x) = 3 x^{2} ln 2 x$ $f(x) = 3x^2 ln 2x$ ?