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3 years ago

F(x) = 4√(2x³-1) F'(x) =.....?

Mathematics

1 answer:

goldfiish [28.3K]3 years ago

6 0

Answer:

$\large\boxed{f'(x)=\dfrac{12x^2}{\sqrt{2x^3-1}}}$

Step-by-step explanation:

$f(x)=4\sqrt{2x^3-1}=4\left(2x^3-1\right)^\frac{1}{2}\\\\f'(x)=4\cdot\dfrac{1}{2}(2x^3-1)^{-\frac{1}{2}}\cdot3\cdot2x^2=\dfrac{12x^2}{(2x^3-1)^\frac{1}{2}}=\dfrac{12x^2}{\sqrt{2x^3-1}}\\\\\text{used}\\\\\sqrt{a}=a^\frac{1}{2}\\\\\bigg[f\left(g(x)\right)\bigg]'=f'(g(x))\cdot g'(x)\\\\\bigg[nf(x)\bigg]'=nf'(x)\\\\(x^n)'=nx^{n-1}$

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All of the sheet with steps please!!

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Answer:

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Step-by-step explanation:

I did half now do the rest! All you have to do is divide or multiply the same as the numerator/denominator!

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3 years ago

Plot A(2,9), B(7,9), C(−3,−5), and D(−3,1) in a coordinate plane. Are AB and CD congruent? if you answer before 11:59 you get br

levacccp [35]

Given :

Four points A(2,9) , B(7,9) , C(-3,-5) and D(-3,1) .

To Find :

Are AB and CD congruent .

Solution :

Two line segment are congruent when their length is equal .

Now , length of line segment with points (a,b) and (c,d) .

$L=\sqrt{(a-c)^2+(b-d)^2}$ .

So , length of AB is :

$AB=\sqrt{(2-7)^2+(9-9)^2}\\\\AB=\sqrt{(-5)^2+0^2}\\\\AB=5\ units$

Also , length of CD is :

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Since , length of AB and CD is not equal .

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4 years ago

Solve cos(2x)=1-sin(x)

Vedmedyk [2.9K]

Given:

$cos(2x)=1-sin(x)$

Expanding using double angle formula,

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Rearranging into a single equation,

$1 - 2 \sin^{2}(x) - 1 + \sin(x) = 0$

Combining like terms,

$- 2 \sin^{2} (x) + \sin(x) = 0$

Now multiplying each term by -1,

$2 \sin^{2} (x) - \sin(x) = 0$

Factor greatest common factors out,

$\sin(x)(2 \sin(x) - 1) = 0$

Applying Zero property rule,

$\sin(x) = 0 \: or \: 2 \sin(x) - 1 = 0$

• Solve the trignometric equation to find a particular solution,

$x = 0 \: or \: x = π$

$= > x = 2nπ \: or \: x = π + 2nπ$

• Find the union of the solution sets,

$x = nπ$ }

• Rearrange unknown terms to the left side,

$2 \sin(x) = 1$

• Divide both sides of the equation by the coefficient of variable,

$\sin(x) = \frac{1}{2}$

• Solve the trignometric equation to find a particular solution,

$x = \frac{π}{6} \: or \: x = \frac{5π}{6}$

$= > x = \frac{π}{6} + 2nπ \: or \: x = \frac{5π}{6} + 2nπ,n∈Z$

}

☆ Now finding the union of both sets

$x = nπ \: or \: x = \frac{π}{6} + 2nπ \: or \: x = \frac{5π}{6} + 2nπ,n∈Z$

Hence, the answer is $x = nπ \: or \: x = \frac{π}{6} + 2nπ \: or \: x = \frac{5π}{6} + 2nπ,n∈Z$

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3 years ago

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ziro4ka [17]

Answer:

2/3,4/3.

Step-by-step explanation:

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3 years ago

Read 2 more answers

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Tamiku [17]

Answer:

x=52

step by step:

x+128=180

x=180-128

x=52 .

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3 years ago