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Evaluate the derivative of the following function?

+1 vote
f(w) = cos[sin^-1(5w)]
asked Feb 21, 2013 in CALCULUS by andrew Scholar

2 Answers

+2 votes

f(w) = cos[sin-1(5w)]

Apply 'derivative with respect to w' each side.

f'(w) = (d/dx){cos[sin-1(5w)]}

Derivative of Trigonometric Functions: (d/dx)[cos(x)] = - sin(x)

f'(w) = - sin[sin-1(5w)][sin-1(5w)]'                                              [inner derivative of sin-1(5w) ]

Derivative of Inverse Trigonometric Functions: (d/dx)sin-1x = 1/√(1 - x2)

f'(w) = - sin[sin-1(5w)][1/√(1 - (5w)2)][5w]'                               [inner derivative of (5w) ]

General Derivative Formulas:(d/dx)(x) = 1.

f'(w) = - sin[sin-1(5w)][1/√(1 - 25w2)][5]

f'(w) = - 5sin[sin-1(5w)] / √(1 - 25w2).

answered Feb 21, 2013 by britally Apprentice
0 votes

 

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Apply 'derivative with respect to w' on each side.

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Apply chain rule in derivatives.

Derivative of Inverse Trigonometric Functions:image

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Derivative of Inverse Trigonometric Functions: image

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answered Jun 21, 2014 by david Expert

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