Question

Determine the first derivative (dy/dx) of y= pie^3 - e^2 + in (x^2 + 2) - piexe^x

Answer 1

Determine the first derivative (dy/dx) of y= pie^3 - e^2 + in (x^2 + 2) - piexe^x

 

y= π^3 - e^2 + ln (x^2 + 2) - πxe^x

since π^3 and e^2 are constant values, then their differential coefficient is zero.

The derivative of ln(x^2 + 2) is

Y’_1 = (1/(x^2 + 2))*(2x + 0) = 2x/(x^2 + 2)

The derivative of πxe^x is

Y’_2 = π(1.e^x + x.e^x) = π.e^x(1  + x)

Then dy/dx = 0 + Y’_1 – y’_2

dy/dx = 2x/(x^2 + 2) - π.e^x(1  + x)