What is the derivative of f(x)=Sin^2 5x + Cos 5x?

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What is the derivative of f(x)=Sin^2 5x + Cos 5x?

2007-11-04 08:15:59 · 2 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics

2 answers

f(x) = [sin (5 x) ] ² + cos (5 x)
f `(x) = 2 [sin ( 5 x ) ](5) cos ( 5 x ) - 5 sin ( 5 x )
f `(x) = 5 sin ( 5x )[ 2 cos 5 x - 1 ]

2007-11-04 10:32:01 · answer #1 · answered by Como 7 · 1⤊ 1⤋

f(x) = sin^2(5x) + cos(5x)

We must use the chain rule. But first, to help for clarification purposes, I'll rewrite it slightly.

f(x) = [ sin(5x) ]^2 + cos(5x)

Taking the derivative gives us

f'(x) = 2[sin(5x)] [cos(5x)] [5] + [ -sin(5x) ] [5]

Which simplifies to

f'(x) = 10sin(5x)cos(5x) - 5sin(5x)

f'(x) = 5sin(5x) [ 2cos(5x) - 1 ]

2007-11-04 08:23:08 · answer #2 · answered by Puggy 7 · 0⤊ 0⤋