Find d/dx?

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Answer 1 · 2018-02-07T04:47:26

The answer is #3cos^2(3x)#

Where #a# is a constant value, we know that:

#d/dx int_a^xf(t)dt = f(x)#

Therefore, using the chain rule, we can say that:

#d/dx int_a^uf(t)dt = f(u) * (du)/dx#

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

In this case, we can let #a=1#, #u = 3x#, and #f(t) = cos^2(t)#.

Therefore:

#d/dx int_1^(3x) cos^2(t)dt = cos^2(3x) * d/dx(3x)#

#= cos^2(3x) * 3#

#= 3cos^2(3x)#

Final Answer