NZ Level 8 (NZC) Level 3 (NCEA) [In development] Chain Rule

## Interactive practice questions

Given that $y=u^3$y=u3 and $u=2x+3$u=2x+3, define $y$y in terms of $x$x. Leave your answer in factored form.

Easy
Less than a minute

Consider the function $f\left(x\right)=\left(5x^3-4x^2+3x-5\right)^7$f(x)=(5x34x2+3x5)7.

Redefine the function as composite functions $f\left(u\right)$f(u) and $u\left(x\right)$u(x), where $u\left(x\right)$u(x) is a polynomial.

Consider the function $f\left(x\right)=\sqrt{2x^2+2x+3}$f(x)=42x2+2x+3.

Redefine the function as composite functions $u\left(x\right)$u(x) and $f\left(u\right)$f(u), where $u\left(x\right)$u(x) is a polynomial.

Consider the function $f\left(x\right)=\frac{1}{\left(4x^2-3x+5\right)^3}$f(x)=1(4x23x+5)3.

Redefine the function as composite functions $f\left(u\right)$f(u) and $u\left(x\right)$u(x), where $u\left(x\right)$u(x) is a polynomial.

### Outcomes

#### M8-11

Choose and apply a variety of differentiation, integration, and antidifferentiation techniques to functions and relations, using both analytical and numerical methods

#### 91578

Apply differentiation methods in solving problems