Question

Find the derivative of y with respect to x, t, or e, as appropriate. y = xnx - 1/2 x 3 0 7x5 x2 O x5-x² + 6x ln x O 6x5-x² Oxnx-x² + 6x5

Answer 1

y = (x^6)*ln(x) - (1/3)*(x^3)

As the function is a function of x, therefore we will differentiate it with respect to x.

Therefore, using chain rule

dy/dx = (x^6)*(1/x) + (ln(x))*6*(x^(6-1)) - (1/3)*(3)*(x^(3-1))

dy/dx = (x^6)*(x^(-1)) + (ln(x))*6*(x^(6-1)) - (1/3)*(3)*(x^(3-1))

dy/dx = x^(6-1) + 6*ln(x)*(x^5) - (x^2)

dy/dx = x^5 - x^2 + 6(x^5)*(ln x)

Therefore, B is the correct option.