## 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

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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