Question

Suppose u and v are functions of x that are differentiable at x=0 and that u(0)=3, u'(0)= -4, v(0)= 2, v'(0)= -7. Find the values of the following derivatives at x=0. A.) d/dx(uv)

Answer 1

`\bf \cfrac{d}{dx}[u(x)\cdot v(x)]\implies \cfrac{du}{dx}\cdot v(x)+u(x)\cdot \cfrac{dv}{dx}\quad \begin{cases} u(0)=3\qquad u'(0)=-4 \\\\ v(0)=2\qquad v'(0)=-7 \end{cases} \\\\ \left[ \cfrac{du}{dx} \right]_(x=0)\cdot v(0)+u(0)\cdot \left[ \cfrac{dv}{dx} \right]_(x=0)`

so.. hmm pretty sure you know what that is