Suppose u and v are differentiable functions of x and

zachutnat4o

zachutnat4o

Answered question

2021-12-04

Suppose u and v are differentiable functions of x and that
u(1) = 2, u'(1) = 0, v(1) = 5, v'(1) = -1.
Find the values of the following derivatives at x = 1.
(d/dx)(uv)

Answer & Explanation

Stephanie Mann

Stephanie Mann

Beginner2021-12-05Added 25 answers

Let g(x)=u(x)v(x)
Using derivative product rule, we have
ddx(uv)=dgdx=g=vdudx+udvdx=vu+uv
We are required to find g'(1).
g'(1)=v(1)u'(1)+u(1)v'(1)
=5(0)+2(-1) [Substituting the given values]
=-2
ddx(uv)x=1=2

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