`y=4x^2 + e^(3x)` find `y'`

y=ln x + e^(2x) find y'

Suppose y=e^(a x)+e^(b x) , find y''

If y=e^(2x) sin3x, find y''.

Find the area bounded by y=-x^(3)+x^(2)+16x and y=4x

If y=4x*root(3)((x^(2)+2)/(3x-7)) , find [(dy)/(dx)]_(x=5)

If x : y = 3 : 4 , then find (3y - x) : (2 x + y) .

If y = 3e^(2x)+2e^(3x) then show that y_2-5y_1 +6y=0

Find the greatest value of x^2 y^3 , where x and y lie in the first quadrant on the line 3x+4y=5 .

Find the compound ratio of the ratios (x + y) : (x - y), (x^(2) + y^(2)) : (x + y)^(2) " and " (x^(2)-y^(2))^(2) : (x^(4) - y^(4)) .

Find a continuous function f, where (x^(4)-4x^(2))lef (x) le (2x^(2)-x^(3)) such that the area bounded by y=f(x), y=x^(4)-4x^(2), the y-axis, and the line x=t," where "(0letle2) is k times the area bounded by y=f(x),y=2x^(2)-x^(3), y-axis, and line x=t("where "0le t le 2).