Suppose u and v are differentiable functions of x and

vakirnarhh

vakirnarhh

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)(u/v)

Answer & Explanation

James Etheridge

James Etheridge

Beginner2021-12-05Added 16 answers

Let g(x)=u(x)v(x)
Using derivative quotient rule, we have
ddx(uv)=dgdx=g=vdudxudvdxv2=vuuvv2
We are required to find g'(1).
g(1)=v(1)u(1)u(1)v(1)(v(1))2
=5(0)2(1)52
=0.08
ddx(uv)x=1=0.08

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