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Chain rule: dV/dh=9h(3h^2+4)^(1/2)
sub in h=0.6 , dV/dh = 12.17

Product rule: first order derivative = 8xlnx+4x Second order derivative = 8lnx+12 Sub in e^2 , 16lne + 12 = 24

We need calculus to find out the properties complex curves that we cannot find with simple arithmetic as we would with linear graphs. Differentiation allows us to calculate the gradient of a curve at a sp...

This is a quadratic equation of the form ax^2 + bx +c, where (t-1)=a 4=b . (t-5)=0 Therefore if there are no real roots, you get that b^2-4ac<0. (using the quadratic formula)

First plug in valu...

This is a good candidate for integration by parts because it is a product of two functions – ln(x) and x^3, and x^3 is easy to integrate. The definition for integration by parts is: integral(u dv/dx) d...