Y = (x²+3)(2x-6) What is the derivative?

Mathematics

1 answer:

ahrayia [7]2 years ago

4 0

Answer:

y = (x²+3)(2x-6)

dy/dx=d(x²+3)(2x-6)/dt=(x²+3)d(2x-6)/dt+(2x-6)d(x²+3)/dt= (x²+3)(2)+(2x-6)(2x)=2x²+6+4x²-12x=6x²-12x+6=6(x²-2x+1)

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Find the derivative of the function by using the Product Rule. Simplify your answer. f(x) = (x - 3)(x + 3)

Morgarella [4.7K]

Answer:

$f'(x)=2x$

Step-by-step explanation:

Given : Function $f(x)=(x-3)(x+3)$

To find : The derivative of the function by using the Product Rule ?

Solution :

The product rule of derivative is

$\frac{d}{dx}(u\cdot v)=uv'+vu'$

Here, u=x-3 and v=x+3

$\frac{d}{dx}((x-3)\cdot (x+3))=(x-3)\frac{d}{dx}(x+3)+(x+3)\frac{d}{dx}(x-3)$

$\frac{d}{dx}((x-3)\cdot (x+3))=(x-3)1+(x+3)1$

$\frac{d}{dx}((x-3)\cdot (x+3))=x-3+x+3$

$\frac{d}{dx}((x-3)\cdot (x+3))=2x$

Therefore, $f'(x)=2x$

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2 years ago

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The team ran

juin [17]

The team ran 2 miles.

Step-by-step explanation:

Step 1; The track is $\frac{3}{4}$ miles long and the team ran 2 $\frac{2}{3}$ laps on it. To calculate the distance run we multiply the number of laps ran with the distance on each lap.

Distance run = Number of laps × Distance on each lap.

Step 2; We convert 2 $\frac{2}{3}$ from a mixed fraction into an improper fraction. To do this, we multiply the whole number with the denominator of the fraction and add with it the numerator of the same fraction whereas the denominator remains unchanged. To convert the fraction 2 $\frac{2}{3}$ = ((2 × 3) + 2) / 3 = $\frac{8}{3}$ .