Question

How do you differentiate
g(x)=x^2secx using the product rule?
full explanation

Answer 1

Answer:

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Answer 2

Step-by-step explanation:

Use Product Rule to find the derivative of ${x}^{2}\sec{x}.$

The product rule states that (fg)'=f'g+fg'.

$\tt \red{ \implies(\frac{d}{dx} {x}^{2}) \sec(x) + {x}^{2} ( \frac{d}{dx} \sec(x)) }$

Use Power Rule: $\frac{d}{dx} {x}^{n}=n{x}^{n-1}$

$\tt \pink{ \implies \: 2x \sec(x) + {x}^{2}( \frac{d}{dx} \sec(x)) }$

Use Trigonometric Differentiation: the derivative of $\sec{x}\: is \:\sec{x}\tan{x}.$

$\boxed{ \tt \purple{ \implies2x\sec{x}+{x}^{2}\sec{x}\tan{x}}}$