AP calculus

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∫[0,x^(3),(t)/√(1+t^(3)),]
Find the derivative of the integral.
A. (3(x^3))/((1+(x^9))^0.5)
B. (x^3)/((1+x^9)^0.5)
C. (3x^3)/((1+x^3)^0.5)
D. (5x^3)/((1+x^6)^0.5)
E. (3x^5)/((1+x^3)^0.5)

I think the answer is A. Can you check my answer please?

  • AP calculus -

    derivative of an integral is the function.

    consider a function f(t)
    and then the integral from t=0 to a
    int f(t) overlimits= INT f(t) at upperlimit- int f(t) at lower limit

    then d/dt INT f(t)= f(upper)-f(lower).

    so here, at t-0, the f(lower)=0
    and then the answer is

    t/sqrt(1-t^3) at t=x^3
    answer B.

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