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How do you calculate the derivative of #int5(sin(t))^5 dt# from #[e^x,5]#?

1 Answer

Aug 11, 2015

# 5 d/dx int_(e^x)^5 sin^5 t dt = = -5 e^x sin^5 (e^x) #

Explanation:

# 5d/dx int_(e^x)^5 sin^5 t dt = -5 d/dxint_5^(e^x) sin^5 t dt #
# = -5 sin^5 (e^x) d/dx(e^x) = -5 e^x sin^5 (e^x) #

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