Given that y=(sin4x)(sec3x), use the product rule to find dy/dx

First, recall the Product rule: f(x)=g(x)*h(x), f'(x)=h(x)*g'(x)+h'(x)*g(x)This reveals the next step, to find the derivatives of our two subsidiary functions(g and h) d/dx * (sin4x) = 4cos(4x) , and d/dx (sec3x)= 3sec(3x)tan(3x) , this one comes from the list of trigonometric identities Now the answer is simple to find by plugging in the values which we have found to our equation. dy/dx= sec3x4cos4x+3sec(3x)tan(3x)*sin4xThis is the answer as required.