Chapter 2: Q 35. (page 222)

Find the derivatives of the functions: $f (x) = x^{2} \log_{2} (x 2^{x})$

Short Answer

Expert verified

The required answer is $3 x^{2} + 2 x \log_{2} x + \frac{x}{\ln 2}$

Step by step solution

Step 1. Given information.

The given function is: $f (x) = x^{2} \log_{2} (x 2^{x})$

Step 2. Find the derivative of the given function.

$f (x) = x^{2} \log_{2} (x 2^{x}) f' (x) = \frac{d}{d x} [x^{2} \log_{2} (x 2^{x})] = \frac{d}{d x} x^{2} [\log_{2} x + \log_{2} (2^{x})] = \frac{d}{d x} x^{2} [\log_{2} x + x] = \frac{d}{d x} x^{3} + \frac{d}{d x} x^{2} \log_{2} x = 3 x^{2} + 2 x \log_{2} x + x^{2} \frac{1}{x \ln 2} = 3 x^{2} + 2 x \log_{2} x + \frac{x}{\ln 2}$

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Find the derivatives of the functions: $f (x) = x^{2} \log_{2} (x 2^{x})$

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Find the derivative of the given function.

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Find the derivatives of the functions: $f (x) = x^{2} \log_{2} (x 2^{x})$