In general, do not use any derivative rules ( as power rule, etc.). Find the derivative...

In general, do not use any derivative rules ( as power rule, etc.). Find the derivative of the following functions at the point "a" by computing average rate of changes for h = ±1, ±0.1, ±0.01, ±0.001, ±0.0001 :

a.) f(x) = x² + x³ , a = 1

b.) f(x) = x ²+ x³ , a = 3

c.) . f(x) = x − x² , a = 2

Expert Solution

milcah answered 2 years ago

A. Use the Product Rule or the Quotient Rule to find the derivative of the function....

A. Use the Product Rule or the Quotient Rule to find the derivative of the function. g(x) = x3 cot(x) + 6x cos(x) B. Use the Product Rule or the Quotient Rule to find the derivative of the function. f(x) = x2 + x − 7 x2 − 7 C. Use the Product Rule or the Quotient Rule to find the derivative of the function. f(x) = (8x2 + 4)(x2 − 6x − 9)

1 = Derivative of a Constant; 2 = Power Rule; 3 = Product Rule; 4 =...

1 = Derivative of a Constant; 2 = Power Rule; 3 = Product Rule; 4 = Quotient Rule; 5 = Derivative of Exponential Function; 6 = Derivative of Logarithmic Function; 7 = Chain Rule 1. Circle the number(s) indicating the rule(s) used to ﬁnd the derivative of each function. Then diﬀerentiate the function. (a.) f(x) = ln7 1 2 3 4 5 6 7 (b.) p(y) = y3.7 1 2 3 4 5 6 7 (c.) g(x) = √x2ex 1...

Find the relative extrema, if any, of the function. Use the second derivative test, if applicable....

Find the relative extrema, if any, of the function. Use the second derivative test, if applicable. (If an answer does not exist, enter DNE.) g(x)=x^3-6x relative maximum (x, y) = ( , ) relative minimum (x, y) = ( , )

The rule of the derivative of a function f is given. Find the location of all...

The rule of the derivative of a function f is given. Find the location of all local extrema. f'(x) = (x2- 1)(x - 2) Group of answer choices Local maxima at -1 and 2; local minimum at 1 Local maximum at 1; local minima at -1 and 2 Local maximum at -1; local minima at -2 and 1 Local maximum at 2 - ; local minimum at 2 +

A) Find the derivative of the function f by using the rules of differentiation. f(x) =...

A) Find the derivative of the function f by using the rules of differentiation. f(x) = 380 B)Find the derivative of the function f by using the rules of differentiation. f(x) = x0.8 C) Find the derivative of the function f by using the rules of differentiation. D)Find the derivative of the function. f(u) = 10 u E)Find the derivative of the function f by using the rules of differentiation. f(x) = 9x3 - 2x2 + 1 u u

Section 3.3 Product and Quotient Rules and Higher-Order Derivatives Find the derivative of the function ...

Section 3.3 Product and Quotient Rules and Higher-Order Derivatives Find the derivative of the function g(s)=√s(s^2+8) g(x)=√x sin⁡x f(x)=x^2/(2√x+1) f(t)=cos⁡t/t^3 y=sec⁡x/x f(x)=sin⁡x cos⁡x y=(2e^x)/(x^2+1) Find equation of the tangent line to the graph of the function f(x)=(x+3)/(x-3) at the point (4, 7) Find the equation of the tangent line to the graph of the function ??=24?3 at the point (1, 2).

Two questions: 2) Use the limit definition of the derivative to find the derivative of f(x)=...

Two questions: 2) Use the limit definition of the derivative to find the derivative of f(x)= x^3 - 9x 3) Using limits, find an equation of the line tangent to the function of g(x)= 4/x^2 at x= -2 Show All Work please! thank you :)

Use the four-step process to find the derivative for: You need to use:

What is the main difference between legal rules from any other kind of rule of conduct...

What is the main difference between legal rules from any other kind of rule of conduct such as moral and religious rules?

1.) Use the product rule to find the derivative of (−10x6−7x9)(3ex+3) 2.) If f(t)=(t2+5t+8)(3t2+2) find f'(t)...

1.) Use the product rule to find the derivative of (−10x6−7x9)(3ex+3) 2.) If f(t)=(t2+5t+8)(3t2+2) find f'(t) Find f'(4) 3.) Find the derivative of the function g(x)=(4x2+x−5)ex g'(x)= 4.) If f(x)=(5−x2) / (8+x2) find: f'(x)= 5.) If f(x)=(6x2+3x+4) / (√x) , . then: f'(x) = f'(1) = 6.) Find the derivative of the function g(x)=(ex) / (3+4x) g'(x)= 7.) Differentiate: y=(ln(x)) /( x6) (dy) / (dx) = 8.) Given that f(x)=x7h(x) h(−1)=2 h'(−1)=5 Calculate f'(−1) 9.) The dose-response for a specific...

Question