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:
248
Step-by-step explanation:
(62)4
= 62 x 4
= 248
A = L^2
A = L^2 = 2^2 + 4^2 (Pythagorean’s theorem)
A = L^2 = 20
Therefore the area of the square is 20 units square.
Answer:
M=p-5n
Step-by-step explanation:
Here we are given that M+5n=p
We are asked to solve this equation for M. In order to do that we will follow these steps.
Subtracting 5n from both sides we get
M+5n-5n=p-5n
M=p-5n
Hence , now we have our M as dependent variable, whose value depends on the values of p and n. One or both of them can be independent variable/.
2.25t+ 5= 13.5t+ 14
⇒ 5- 14= 13.5t- 2.25t
⇒ -9= 11.25t
⇒ -9/11.25= t
⇒ -0.8= t
Final answer: t= -0.8~
