MediumDifferentiation rules

Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) §2.4 The Derivative of the Sine and Cosine, #22 · Calculus · Differentiation rules

For …, the ratio … is … \frac{\sin 2(x+h)-\sin 2x}{h} = \frac{\sin…

For $y = sin 2 x$ , the ratio $Δ y / h$ is
$\frac{sin 2 ( x + h ) - sin 2 x}{h} = \frac{sin 2 x ( cos 2 h - 1 ) + cos 2 x sin 2 h}{h} .$
Explain why the limit $d y / d x$ is $2 cos 2 x$ .

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Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) · §2.4 The Derivative of the Sine and Cosine, #22

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