What is the product rule in differentiation?
The product rule is a special rule that exists for differentiating products of two (or more) functions. It states: If y=uv, then dy/dx= u(dv/dx) + v(du/dx). So when we have a product to differentiate we can use this formula.For example, suppose we want to differentiate y=x2(cos3x). In this question u=x2 and our v=cos(3x). So following the formula, our first step is to differentiate the u and v terms. du/dx=2x and dv/dx= -3sin(3x). We now put all these results into the given formula:dy/dx= u(dv/dx) + v(du/dx) = x2 x (-3sin3x) + 2x x cos3x We can tidy this answer up by noticing there is a common factor of x giving us this as a final answer: dy/dx= x(-3xsin3x+ 2cos3x )
IA
Related Maths A Level answers
All answers ▸Solve the equation |3x + 4| = |3x - 11|
Find ∫ ( 2x^4 - 4x^(-0.5) + 3 ) dx
By expressing cos(2x) in terms of cos(x) find the exact value of the integral of cos(2x)/cos^2(x) between the bounds pi/4 and pi/3.
Why is the definite integral between negative limits of a function with positive values negative even though the area bound by the x-axis is positive? for example the integral of y=x^2 between x=-2 and x=-1