MediumDifferentiation rules

Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) §2.4 The Derivative of the Sine and Cosine, #20 · Calculus · Differentiation rules

Find the derivative of … in two ways: (a) Expand to

Find the derivative of $sin (x + 1)$ in two ways:
(a) Expand to $sin x cos 1 + cos x sin 1$ . Compute $d y / d x$ .
(b) Divide $Δ y = sin (x + 1 + Δ x) - sin (x + 1)$ by $Δ x$ . Write $X$ instead of $x + 1$ . Let $Δ x$ go to zero.

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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, #20

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