Differentiate the equation y = x^2 + 3x + 1 with respect to x.
A simple way to differentiate an equation with respect to x is to reduce each x components power by one and multiply each x component by their original power.
Looking at the equation y = x^2 + 3x + 1, the component x^2 will be reduced from a power of 2 to a power of 1 and multiplied by its original power 2 to give 2x. The component 3x is reduced from a power of 1 to a power of zero and multiplied by its original power of 1 to give 3. As 1 is a constant and not an x component it dissapears in the differentiated eqution.
This therefore gives an answer of dy/dx = 2x + 3.
JB
Related Maths A Level answers
All answers ▸The curve has equation y = x^3 - x^2 - 5x + 7 and the straight line has equation y = x + 7. One point of intersection, B, has coordinates (0, 7). Find the other two points of intersection, A and C.
By consdering partial fractions find the integral of (1-x)/(5x-6-x^2) between x = 1 and x = 0, give your answer in an exact form.
Find the values of x for which f(x) is an increasing function given that f(x)=8x-2x^2
Where does integration by parts come from?