Plz help me it’s important

Derivative of this function<br> <br>Y= -7X³ -8X² +6X +3

zaharov [31]

In general, the derivative of a single term Ax^(n) is A n x^(n-1) .

And the derivative of a sum of many terms is the sum of the derivatives
of the individual terms.

Using these two rules, the derivative (with respect to 'x') of the expression
in the question is . . .

<em> Y' = -21x² - 16x + 6</em>

7 0

3 years ago

What is 36.32 rounded to the nearest whole number

s2008m [1.1K]

Answer:

It is 36. This is because you round down.

Step-by-step explanation:

8 0

3 years ago

Read 2 more answers

A quadratic function y=f(x)y=f(x) is plotted on a graph and the vertex of the resulting parabola is (5, -6)(5,−6). What is the v

MariettaO [177]

Answer:

The vertex is at (5,4).

Step-by-step explanation:

I graphed both of the functions on the graph below.

If this answer is correct, please make me Brainliest!

5 0

3 years ago

Which of the following equations is paralllel to the line y+3x+1 and passes through the point (6,-3)

RideAnS [48]

Answer:

y=3x-21

Step-by-step explanation:

a line is parallel if the slopes of the lines are the same

so that means that out line should look something like this

y=3x+b

then, we use our point given to find b

-3=18+b

b=-21

the equation of out line is y=3x-21

7 0

3 years ago

Find the integral using substitution or a formula.

Nadusha1986 [10]

$\rm \int \dfrac{x^2+7}{x^2+2x+5}~dx$

Derivative of the denominator:
$\rm (x^2+2x+5)'=2x+2$

Hmm our numerator is 2x+7. Ok this let's us know that a simple u-substitution is NOT going to work. But let's apply some clever Algebra to the numerator splitting it up into two separate fractions. Split the +7 into +2 and +5.

$\rm \int \dfrac{x^2+2+5}{x^2+2x+5}~dx$

and then split the fraction,

$\rm \int \dfrac{x^2+2}{x^2+2x+5}~dx+\int\dfrac{5}{x^2+2x+5}~dx$

Based on our previous test, we know that a simple substitution will work for the first integral: $\rm \quad u=x^2+2x+5\qquad\to\qquad du=2x+2~dx$

So the first integral changes,

$\rm \int \dfrac{1}{u}~du+\int\dfrac{5}{x^2+2x+5}~dx$

integrating to a log,

$\rm ln|x^2+2x+5|+\int\dfrac{5}{x^2+2x+5}~dx$

Other one is a little tricky. We'll need to complete the square on the denominator. After that it will look very similar to our arctangent integral so perhaps we can just match it up to the identity.

$\rm x^2+2x+5=(x^2+2x+1)+4=(x+1)^2+2^2$

So we have this going on,

$\rm ln|x^2+2x+5|+\int\dfrac{5}{(x+1)^2+2^2}~dx$

Let's factor the 5 out of the intergral,
and the 4 from the denominator,

$\rm ln|x^2+2x+5|+\frac54\int\dfrac{1}{\frac{(x+1)^2}{2^2}+1}~dx$

Bringing all that stuff together as a single square,

$\rm ln|x^2+2x+5|+\frac54\int\dfrac{1}{\left(\dfrac{x+1}{2}\right)^2+1}~dx$

Making the substitution: $\rm \quad u=\dfrac{x+1}{2}\qquad\to\qquad 2du=dx$

giving us,

$\rm ln|x^2+2x+5|+\frac54\int\dfrac{1}{\left(u\right)^2+1}~2du$

simplying a lil bit,

$\rm ln|x^2+2x+5|+\frac52\int\dfrac{1}{u^2+1}~du$

and hopefully from this point you recognize your arctangent integral,

$\rm ln|x^2+2x+5|+\frac52arctan(u)$

undo your substitution as a final step,
and include a constant of integration,

$\rm ln|x^2+2x+5|+\frac52arctan\left(\frac{x+1}{2}\right)+c$

Hope that helps!
Lemme know if any steps were too confusing.

8 0

3 years ago