Question

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 2 3 4 5 6 7
(d.) j(z) = 1 z2+1 1 2 3 4 5 6 7
(e.) h(x) = x lnx 1 2 3 4 5 6 7
2. Simplify each function, if possible. All exponents should be positive and factor out common factors. Do not find the derivative

. (a.) f(x) = x−4(x + 6)5

(b.) g(x) = e9x(x−2)2 + 9e9x(x−2)

(c.) h(x) = x x+2

Answer 1

1(a)

As we know ln(7) is constant.

So we can use 1 rule t find its derivative.

(b)

It is a exponent of variable. So we can use Rule 2 : Power rule to find its derivative.

(c)

It is a product of two functions. So we will use Product rule , Rule 3 to find its derivative.

(d)

In this we can use power rule to fid its derivative. So we will use Rule 2 .

(e)

It is product of two function. So we will use rule 3 to find its derivative.

2(b)

  

  

  

(c)