Today's Takeaway

Simple

100

This is the name of the process used to find the slope of a curve at any point.

Differentiation

200

The derivative of a constant number is always this. 

Zero

300

The derivative of y = x^-2 with respect to x is this.

-2x^-3

Medium

100

If y=3x^-3+2x, find dy/dx.

-9x^-4 + 2

200

A water tank in Dubai fills at a rate modeled by V(t)=4t+10. Find dV/dt

4

300

Find dy/dx for y=x⁴−4x²+7

4x³ -8x  

Harder

100

Electricity consumption in a house is E(t)=50+5t². Find the rate of change at t=4 hours.

40 Units

200

A water bottle is filled at a steady rate. If the volume v in liters after tminutes is V(t)=2t+1, what is the slope of the graph at any time?

2 liters per minute.

300

The temperature in Dubai changes during the day. If the temperature in °C at time t hours is T(t)=0.5t²+25, what does the derivative dT/dt represent?

The rate at which the temperature changes per hour.