If y = 5x^3 - 2x^2 + 2, what is dy/dx?
Differentiation can be done term-by-term, so we can treat the 5x3, -2x2 and 2 separately. We can also 'take out' the coefficients: to differentiate 5x3, for example, differentiate x3 first and then multiply by 5.
For the first term: x3 differentiates to 3x2, so we get 15x2.
Second term: x2 differentiates to 2x, so we have -4x.
Third term: The derivative of a constant is zero.
The answer is just the sum of these, which is 15x2 - 4x.
AK
Related Maths A Level answers
All answers ▸Solve the following equation, give the answer/answers as coordinates. y=3x^2 , y=2x+5.
A curve has an equation of y = 20x - x^2 - 2x^3, with one stationary point at P=-2. Find the other stationary point, find the d^2y/dx^2 to determine if point P is a maximum or minium.
John wants to separate a rectangular part of his garden for his puppy. He has material for a 100-meter long fence and he plans to use one side of his house as a barrier. How should John select the sizes of his fence in order to gain the biggest territory?
Differentiate with respect to x: y = ln(x^2+4*x+2).