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:
B
Step-by-step explanation:
hope this helps
Answer:
Infinity minus 9 is infinity-9
Step-by-step explanation:
Answer:
95.5°F
Step-by-step explanation:
Given the regression equation :
y = 1.8x - 76.9 ; the relationship between temperature (°F) and number of ice cream sold
y = number of ice cream sold
x = temperature (°F)
The temperature when 95 iccream cones are sold will be ;
Here, y = 95
Using the model :
95 = 1.8x - 76.9
95 + 76.9 = 1.8x
171.9 = 1.8x
Divide both sides by 1.8
171.9 / 1.8 = x
95.5°F = x
Hence, temperature when 95 cones of ice-cream are sold is 95.5°F
