Find the derivative with respect to x of the integral from 2 to x squared of the cosine of the quantity t squared plus 1, dt

Question

Find 

 – 2xsin(x⁴ + 1) 

2xcos(x⁴ + 1) 

– 4x³ sin(x⁴ + 1) 

4x³ cos(x⁴ + 1)

Answer 1

d/dx [∫_{(from 2 to x}²(cos(t² + 1))dt] = cos[(x²)² + 1] d/dx(x²) = 2xcos(x⁴ + 1)