IB Maths SL, Differentiation Chain Rule

Algebra, Functions and equations, Circular functions and trigonometry, Vectors, Statistics and probability, Calculus. IB Maths SL Revision Notes

IB Maths SL, Differentiation Chain Rule

IB Mathematics SL – Derivatives, Differentiation Chain Rule

How can we find the first derivative function of $h(x)=sin(5x)$ ??

Thanks
Oliver

Posts: 0
Joined: Mon Jan 28, 2013 8:08 pm

IB Mathematics SL, Differentiation Chain Rule

IB Mathematics SL – Calculus, Derivatives, Differentiation Chain Rule

We know that the derivative of composite functions is given by the following formula

$[f(g(x))]'=f'(g(x))g'(x)$

The chain rule states that the derivative of a function of a function (composite function) equals derivative of the outer function times derivative of the inner function.

So about your question we view $h(x)$ as a composite function $f(g(x))$ , where $f(y)=sin(y) \and\ g(x)=5x$.

Using the Chain rule we obtain
$h'(x)=(sin(5x))'=$

$=cos(5x) (5x)'=5cos(5x)$

Hope these help!!
miranda

Posts: 268
Joined: Mon Jan 28, 2013 8:03 pm

Re: IB Maths SL, Differentiation Chain Rule

thank you miranda!!
Oliver

Posts: 0
Joined: Mon Jan 28, 2013 8:08 pm