MediumDifferentiation rules

Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) §2.4 The Derivative of the Sine and Cosine, #26 · Calculus · Differentiation rules

True or false, with reason: (a) The derivative of … is …

True or false, with reason:
(a) The derivative of $sin^{2} x$ is $cos^{2} x$
(b) The derivative of $cos (- x)$ is $sin x$
(c) A positive function has a negative second derivative.
(d) If $y^{'}$ is increasing then $y^{''}$ is positive.

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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, #26

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