Differentiate the following: y=(7x^2+2)sinx
Differentiate using the product rule.Product rule: for y=uv , where u and v are functions of x, dy/dx=vdu/dx + udv/dxy=(7x2+2)sinx so u=(7x2+2) and v=sinx . By differentiating these functions:du/dx=14x and dv/dx=cosxnow we have expressions for u, v, du/dx and dv/dx, we can find dy/dx.Recall dy/dx=vdu/dx + udv/dx, by substituting our expressions:dy/dx=14xsinx +(7x2+2)cosx
