Differentiate.
-f(x) = tan(cos x)
A) -sin x $\sec ^ { 2 }$ (cos x)
B) $\sec ^ { 2 }$ (cos x)
C) tan(-sin x)
D) tan(cos x) sec(cos x)
E) none of these

Name: Differentiate. -f(x) = tan(cos x) A) -sin x $\sec ^ { 2 }$ (cos x) B) $\sec ^ { 2 }$ (cos x) C) tan(-sin x) D) tan(cos x) sec(cos x) E) none of these
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Question

Differentiate. 
-f(x) = tan(cos x)
A) -sin x $\sec ^ { 2 }$ (cos x)
B) $\sec ^ { 2 }$ (cos x)
C) tan(-sin x)
D) tan(cos x) sec(cos x)
E) none of these

Quizplus · Accepted Answer

The derivative of tan(u) is sec^2(u) * du/dx. Here, u = cos(x), so du/dx = -sin(x). Therefore, the derivative is sec^2(cos(x)) * (-sin(x)), which matches choice A.

Differentiate sec⁡2\sec ^ { 2 }sec2 (Cos X) B) sec⁡2\sec ^ { 2 }sec2

Differentiate $\sec ^ { 2 }$ (Cos X)
B) $\sec ^ { 2 }$