Differentiation Chain Rule Starter Explain what differentiation is

Differentiation: Chain Rule • Starter: Explain what differentiation is Explain how to find a tangent of a function f(x) Explain how to find a stationary point of a function f(x)

The whole function is raised to a power Multiply by the power and reduce it by 1 ‘as usual’ Also multiply by f’(x)

CHAIN RULE This is another form of the Chain Rule y is a function of u, and u is a function of x WORKING OUT SPACE Differentiate in terms of x Differentiate in terms of u

WORKING OUT SPACE Differentiate in terms of x Differentiate in terms of u

WORKING OUT SPACE Differentiate in terms of x Differentiate in terms of u

WORKING OUT SPACE Let u be the part under the square root, and differentiate Differentiate in terms of u

WORKING OUT SPACE Let u be the part under the square root, and differentiate Differentiate in terms of u

WORKING OUT SPACE Let u be the part under the square root, and differentiate Differentiate in terms of u

WORKING OUT SPACE Let u be the part under the square root, and differentiate Differentiate in terms of u

USING: This is a particular case of differentiating… WB 4 a and find the gradient at the point (2, 1), Differentiate, only ‘the other way round’ (no real difference…) Invert the answer to get dy/ dx Sub in the y-coordinate since the equation is in terms of y (you’re used to only using x) And work it out!

WB 4 b and find the gradient at the point (1, 4), WORKING OUT SPACE Let u be the part under the square root, and differentiate Differentiate in terms of u

self-assess using: R / A / G ‘I am now able to ____. To improve I need to be able to ____’