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Sodium chlorate crystals are easy to grow in the shape of cubes by allowing a solution of water and sodium chlorate to evaporate slowly. If V is the volume of such a cube with side length x, calculate the derivative when x = 5 mm. V'(5) = 27 Incorrect: Your answer is incorrect. mm3/mm

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lublana

Answer:

V'(x) =[tex]75mm^3/mm[/tex]

Step-by-step explanation:

We are given that

Side of cube=x

We have to find the derivative when x=5 mm

We know that

Volume of cube,V=[tex](side)^3[/tex]

Using the formula

[tex]V=x^3[/tex]

Differentiate w.r.t x

[tex]V'(x)=3x^2[/tex]

By using the formula

[tex]\frac{dx^n}{dx}=nx^{n-1}[/tex]

[tex]V'(x)=3(5)^2=75mm^3/mm[/tex]

Hence, the derivative,V'(x) =[tex]75mm^3/mm[/tex]

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