Differentiate y=x^4sinx
- Firstly, we must recognise that the function is in the form of a product, y=uv, where u and v are functions of x. Therefore, we can use the product rule, dy/dx = u (dv/dx) + v (du/dx). 2) We can write u = x^4 and differentiating this we obtain du/dx = 4x^3 by multiplying by the power then taking one off the power (the general rule for differentiation being y=ax^n, dy/dx = anx^(n-1). 3) We then take v= sinx and differentiating this we obtain dv/dx = cosx. 4) The product rule then gives, dy/dx = u (dv/dx) + v (du/dx) = x^4cosx + 4x^3sinx. 5) Simplifying this then gives, dy/dx = x^3 (xcosx + 4sinx).
