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:
Rational numbers' decimal representations either finish or repeat a pattern. Divide the top by the bottom, the numerator by the denominator to convert fractions to decimals, and if the division doesn't come out evenly, round off after a specific number of decimal places.
Step-by-step explanation:
Answer:
\sqrt(3)[cos((4\pi )/(45))+isin((4\pi )/(45))]
Step-by-step explanation:
The first one.
Answer:
512 is equivalent
Step-by-step explanation:
2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2=2^9
2^9=512
Answer:
14.3
Step-by-step explanation:
9/5= 9.2/x (cross multiply)
5 x 9.2= 46
46 ÷ 9 = 5.1
9.2 + 5.1 = 14.3
