Final answer to the problem
$2x\cos\left(x^2\right)$
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Step-by-step Solution
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1
Apply the trigonometric identity: $\frac{d}{dx}\left(\sin\left(\theta \right)\right)$$=\frac{d}{dx}\left(\theta \right)\cos\left(\theta \right)$, where $x=x^2$
$\frac{d}{dx}\left(x^2\right)\cos\left(x^2\right)$
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$\frac{d}{dx}\left(x^2\right)\cos\left(x^2\right)$
Learn how to solve problems step by step online. d/dx(sin(x^2)). Apply the trigonometric identity: \frac{d}{dx}\left(\sin\left(\theta \right)\right)=\frac{d}{dx}\left(\theta \right)\cos\left(\theta \right), where x=x^2. Apply the formula: \frac{d}{dx}\left(x^a\right)=ax^{\left(a-1\right)}, where a=2. Apply the formula: a+b=a+b, where a=2, b=-1 and a+b=2-1.
Final answer to the problem
$2x\cos\left(x^2\right)$
