Problemas
Find (dy)/(dx) at (-6,1) if xy=(6^y)/(x+5) . (Rc
Roztwór
Hugo
élite · Tutor durante 8 años
4
(260 Votos)
Respuesta
To find
at \((-6, 1)\) for the equation
, we need to implicitly differentiate the given equation with respect to
.Given:
First, let's rewrite the equation for clarity:
Now, differentiate both sides with respect to
:
Using the product rule on the left side:
Now, apply the quotient rule to the right side:
Next, differentiate
with respect to
:
And differentiate
with respect to
:
Substitute these into the equation:
Simplify the right side:
Factor out
on the right side:
Combine terms:
Factor out
on the right side:
Combine terms:
Factor out
on the right side:
Combine terms:
Factor out
on the right side:
Combine terms:
Factor out
on the right side:\[ y + x \frac{dy}{dx} = \frac{6^y \ln(6) \cdot \frac{dy}{dx} (x+5) - 6^y}{(x+