Find the derivative of the following expression: y=x^3+2x^2+6x+5.
As the expression contains 4 separate terms that are added together, we can treat this as 4 separate differentiations. The general rule for differentiation for a general term bx^n is (bn)x(n-1). For example, the first differentiation in this question is for x3, which would lead to (31)x(3-1), as b is just 1, which can be simplified to 3x2. Carrying on, we can find the following differentiations, which are:
2x2 goes to 4x
6x goes to 6
5 goes to 0
The final differentiation is 0 due to the fact that while it is written in the question as 5, we can actually think of it as 5x0. This is due to the fact that anything to the power of 0 is 1, leaving just 5. Using the general rule again, this would give the result of (5*0)x(0-1) = 0.
The final result is therefore dy/dx = 3x2+4x+6.
Related Maths A Level answers
All answers ▸Differentiate x^x
How do I integrate sin^2(x)?
g(x) = e^(x-1) + x - 6 Show that the equation g(x) = 0 can be written as x = ln(6 - x) + 1, where x<6
A smooth 4g marble is held at rest on a smooth plane which is fixed at 30 degrees to a horizontal table. The marble is released from rest - what speed is the marble travelling at 5 seconds after being released? Let g = 9.8ms^2