izvodi

Question 1

What is the first derivative of the function ( y = C )?

Answer 1

y’ = 0

Question 2

What is the first derivative of the function ( y = x )?

Answer 2

y’ = 1

Question 3

What is the first derivative of the function ( y = x^n )?

Answer 3

y’ = nx^{n-1}

Question 4

What is the first derivative of the function ( y = a^x )?

Answer 4

y’ = a^x ln a

Question 5

What is the first derivative of the function ( y = e^x )?

Answer 5

y’ = e^x

Question 6

What is the first derivative of the function ( y = log_a x )?

Answer 6

y’ = \frac{1}{x ln a}

Question 7

What is the first derivative of the function ( y = ln x )?

Answer 7

y’ = \frac{1}{x}

Question 8

What is the first derivative of the function ( y = sqrt{x} )?

Answer 8

y’ = \frac{1}{2sqrt{x}}

Question 9

What is the first derivative of the function ( y = \frac{1}{x} )?

Answer 9

y’ = -\frac{1}{x^2}

Question 10

What is the first derivative of the function ( y = sin x )?

Answer 10

y’ = cos x

Question 11

What is the first derivative of the function ( y = cos x )?

Answer 11

y’ = -sin x

Question 12

What is the first derivative of the function ( y = an x )?

Answer 12

y’ = \frac{1}{cos^2 x}

Question 13

What is the first derivative of the function ( y = cot x )?

Answer 13

y’ = -\frac{1}{sin^2 x}

Question 14

What is the first derivative of the function ( y = arcsin x )?

Answer 14

y’ = \frac{1}{sqrt{1-x^2}}

Question 15

What is the first derivative of the function ( y = arccos x )?

Answer 15

y’ = -\frac{1}{sqrt{1-x^2}}

Question 16

What is the first derivative of the function ( y = arctan x )?

Answer 16

y’ = \frac{1}{1+x^2}

Question 17

What is the first derivative of the function ( y = ext{arccot } x )?

Answer 17

y’ = -\frac{1}{1+x^2}