Differentiate y = 15x^3 + 24x^2 + 6 with respect to x.
To differentiate y with respect to x, you have to multiply each x term by their respective power and then decrease their power by one. For example, 4x2 differentiated is 2 x 4x2-1 = 8x. So, splitting this problem into parts, 15x3 differentiated is 3 x 15x3-1 = 45x2, and 24x2 differentiated is 48x. 6 doesn't involve x so it cannot be differentiated with respect to it. Hence, dy/dx = 45x2 + 48x.
DM
Related Maths A Level answers
All answers ▸Differentiate the equation 4x^5 + 2x^3 - x + 2
Find the gradient of the equation y=e^2x.ln(4x^2) when x=5.
Sine Rule
y = 4x/(x^2+5). a) Find dy/dx, writing your answer as a single fraction in its simplest form. b) Hence find the set of values of x for which dy/dx < 0