Thursday, 7 January 2016

The Product Rule of Differentiation - Example x^2 tan(x)



In this video, we find the differential of the function x2tan(x) by considering it as a product of 2 functions, x2 and tanx. This allows us to apply a method called the Product Rule, which helps us to find the derivative with relative ease.

The product rule is defined as:
\frac{\mathrm{d} }{\mathrm{d} x}\left ( u\cdot v \right )=v\frac{\mathrm{d} u}{\mathrm{d} x}+u\frac{\mathrm{d} v}{\mathrm{d} x}
Or in shorthand form:
\left (u\cdot v \right )'=vu'+uv'
So if we let...
u = x2
v = tan(x)
The derivatives of u and v are...
du/dx = u' = 2x
dv/dx = v' = sec2(x)
We can then substitute these terms accordingly into the product rule to find the derivative of x2tan(x)

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