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First we must find the gradient of the curve at the point (1, 4) - we do this by finding the derivative dy/dx, as we do to find any gradient. Differentiating the equation of the curve gives us that dy/dx ...

Integrating by parts requirez recognition that ln(x) is equal to ln(x) multiplied by 1. Making u equal to ln(x) should make the integration trivial. Differentiation is a simple use of the product rule and...

First, let's make y the subject of the equation.

Let's achieve this by having only y on the left hand side of the equation. To do this we need to minus 3x from both sides of the equation. This leav...

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