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nexus9112 [7]
2 years ago
7

After a wholesaler adds a markup of $125 to a stereo, it is sold for $320. What is the cost of the stereo?

Mathematics
1 answer:
notka56 [123]2 years ago
7 0

Answer:

$ 195

Step-by-step explanation:

let the cost of stereo ne x

wholesaler add markup = 125

sold on = 320

so,

x+ 125 = 320

x = 320 -125

x = $195

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————————

You can actually use either the product rule or the chain rule for this one. Observe:

•  Method I:

y = cos² x

y = cos x · cos x


Differentiate it by applying the product rule:

\mathsf{\dfrac{dy}{dx}=\dfrac{d}{dx}(cos\,x\cdot cos\,x)}\\\\\\&#10;\mathsf{\dfrac{dy}{dx}=\dfrac{d}{dx}(cos\,x)\cdot cos\,x+cos\,x\cdot \dfrac{d}{dx}(cos\,x)}


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\therefore~~\boxed{\begin{array}{c}\mathsf{\dfrac{dy}{dx}=-2\,sin\,x\cdot cos\,x}\end{array}}\qquad\quad\checkmark

—————

•  Method II:

You can also treat  y  as a composite function:

\left\{\!&#10;\begin{array}{l}&#10;\mathsf{y=u^2}\\\\&#10;\mathsf{u=cos\,x}&#10;\end{array}&#10;\right.


and then, differentiate  y  by applying the chain rule:

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and then you get the same answer:

\therefore~~\boxed{\begin{array}{c}\mathsf{\dfrac{dy}{dx}=-2\,sin\,x\cdot cos\,x}\end{array}}\qquad\quad\checkmark


I hope this helps. =)


Tags:  <em>derivative chain rule product rule composite function trigonometric trig squared cosine cos differential integral calculus</em>

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