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 ▸Showing all your working, evaluate ∫ (21x^6 - e^2x- (1/x) +6)dx
A cubic polynomial has the form p(z)=z^3+bz^2+cz+d, z is Complex and b, c, d are Real. Given that a solution of p(z)=0 is z1=3-2i and that p(-2)=0, find the values of b, c and d.
By writing tan x as sin x cos x , use the quotient rule to show that d dx ðtan xÞ ¼ sec2 x .
Differentiate: 2(x^2+2)^3