Answer to Question #205065 in Calculus for Akhona Klanisi

Question

Question 1

Find the derivative of

y = ln 3x⁵.

 

a.    ln 3x⁵

b.    15x⁴

c.    5x⁻¹

d. 1/

3x⁵

 

Question  2

Find the derivative of the function

a.    x²_/ x + x_/ x

b. x² + x /x

c. 2x + 1

d.    3x⁴ + 2x³

 

Question  3

Differentiate the function

f (x) = 3x³e^2x.

a. 5x⁴e^3x

b. 3x²e^2x(x − 3)

c. 3e^3x + 9x⁴x⁵

d. 3x²e^2x(2x + 3)

Question  4

The total revenue function (TR), in terms of P and the company's quantity, if a commodity sells for R199.00  are?

a. TR = 6 000 − 30P ; Q = 30.

b. TR = 6 000P − 30P ²; Q = 30.

c. TR = P (6 000 − 30P ); Q = 24.

d.  TR = 6 000 − 30P ; Q = 24.

 

Answer 1

1.

$y' =\frac{15x^4}{3x^5}=5x^{-1}$

Answer: c. 5x⁻¹

2.

$y=x^2+x$

$y'=2x+1$

Answer: c. 2x + 1

3.

$f' (x) =9x^2e^{2x}+ 6x^3e^{2x}=3x^2e^{2x}(2x + 3)$

Answer: d. 3x²e^2x(2x + 3)

4.

The total revenue function (TR), in terms of P and the company's quantity, if a commodity sells for R199.00 are?

$TR = Q P = 6 000 P - 30 P^2$

$Q = 6 000 - 30 P = 6 000 - 30 \cdot199 = 30$

Answer: b. TR = 6 000P − 30P ²; Q = 30