Question

What is \[\frac{df}{dx}\] for \[f(x)=\sin(x^2)\]?

Options

• \[2x\sin(x^2)\]

• \[2x\cos(x^2)\]

• \[\cos(x^2)\]

• \[\sin(2x)\]

Answer 1

Differentiate the outer function \[\sin t\] to obtain \[\cos t\]. Since \[\frac{dt}{dx}=2x\], the derivative is \[2x\cos(x^2)\].