Taking the derivative of 7 times secant of x^3:
We take out 7 as a constant focus on secant (x^3)
To take the derivative, we use the chain rule, taking the derivative of the inside, bringing it out, and then the derivative of the original function. For example:
The derivative of x^3 is 3x^2, and the derivative of secant is tan(x) and sec(x).
Knowing this: secant (x^3) becomes tan(x^3) * sec(x^3) * 3x^2. We transform tan(x^3) into sin(x^3)/cos(x^3) since tan(x) = sin(x)/cos(x). Then secant(x^3) becomes 1/cos(x^3) since the secant is the reciprocal of the cosine.
We then multiply everything together to simplify:
sin(x^3) * 3x^2/ cos(x^3) * cos(x^3) becomes
3x^2 * sin(x^3)/(cos(x^3))^2
and multiplying the constant 7 from the beginning:
7 * 3x^2 = 21x^2, so...
our derivative is 21x^2 * sin(x^3)/(cos(x^3))^2
Answer:
second one is 3, the last one is 4560
Step-by-step explanation:
It is a percent increase and it increased by 15%
I got this answer by doing 24.61/21.40 which equals 1.15
You can check this answer by doing 21.40 * .15 on a calculator and when you do this you get 3.21 which you can then add back to 21.40 to get $24.61
Answer:
x=1, y=-6. (1, -6).
Step-by-step explanation:
y=-6x
-2x-7y=40
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-2x-7(-6x)=40
-2x+42x=40
40x=40
x=40/40
x=1
y=-6(1)=-6
