Differentiate with respect to x y=(x^3)ln2x
To be able to differentiate this we need to use the product rule as we want to differentiate two functions multiplied together. The product rule states that if y=uv, then : dy/dx= u dv/dx + v du/dx. Let u= x^3 and v= ln2x. Then du/dx= 3x^2 and dv/dx= 2/2x. Putting this together using the formula gives: dy/dx= x^3 * 2/2x + ln2x * 3x^2. This simplifies to dy/dx= 3x^2ln2x+x^2
JP
Related Maths A Level answers
All answers ▸Calculate the volume of revolution generated by the function, f(x) = (3^x)√x, for the domain x = [0, 1]
Express root(125^x)/5^(2x-1) in terms of 5^a where a is an expression in terms of x.
Simplify ln(e^2) - 4ln(1/e)
Differentiate with respect to x: 3 sin^2 x + sec 2x