find the derivative of the question below.

Question

f(x)= ₀∫^√xcos(t) dt

df/dx=?

Answer 1

Hi Rana,

When you take the derivative of an integral, you apply the Fundamental Theorem of Calculus (FTC).

In this case, df/dx of ∫₀^√xcos(t)dt is cos(√x)*(1/(2√x))

* You simply plug in the value of the bounds into the function and apply the chain rule to the bounds, if applicable. (If you plug in the lower bound, be sure to insert a negative sign.) Note that the lower bound in the problem is zero; -cos(0)*0=0. So whenever you have a constant, it's always zero due to the chain rule.

I hope this helps!