Find dy/dx when y = 5x^6 + 4x*sin(x^2)

Looking at the first element of the equation 5x⁶, we can simply multiply 6 by 5 to give 30 and subtract 1 from the power of x. So d/dx[5x⁶] = 30x⁵. The next element of the equation is 4xsin(x²), where we will need to use the product rule (since we have the variable x in both 4x and sin(x²) which are being multiplied) and chain rule (for sin(x²) since this is the composition of the two functions sin() and x²). From the product rule we obtain 4sin(x²) + 4xd/dx[sin(x²)]. Using the chain rule to differentiate sin(x²), we get cos(x²)d/dx[x²] = 2xcos(x²). Therefore our end result for dy/dx = 30x⁵ + 4sin(x²) + 4x2xcos(x²) = 30x⁵ + 4*sin(x²) + 8x²*cos(x²)