New Zealand
Level 8 - NCEA Level 3

# Applications of differentiation of various functions

## Interactive practice questions

Find the equation of the tangent to the curve $y=e^x-3\sin x$y=ex3sinx at $x=\frac{3\pi}{2}$x=3π2.

Easy
Approx 9 minutes

Find the equation of the tangent to the curve $y=e^{\cos x}$y=ecosx at the point $x=\frac{3\pi}{2}$x=3π2.

The curve $y=x\cos x$y=xcosx passes through the point $Q$Q, $\left(\frac{\pi}{2},0\right)$(π2,0).

Find the equation of the tangent at point $Q$Q.

The displacement of a particle moving in rectilinear motion is given by $x\left(t\right)=\left(t-2\right)^2+\sin\left(t-4\pi\right)+3t+25$x(t)=(t2)2+sin(t4π)+3t+25.

### 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