Quadratics

Question 0

Find the derivative of Sin(ax)

Answer 0

a.cos(ax)

Question 1

Find the derivative of ax^n.

Answer 1

n.ax^n-1

Question 2

Find the derivative of Cos(ax)

Answer 2

-a.sin(ax)

Question 3

Find the derivative of ln(ax)

Answer 3

1/ax

Question 4

Find the derivative of e^ax

Answer 4

a.e^ax

Question 5

Find the integral of ax^n

Answer 5

ax^n+1
_______ +C
n+1

Question 6

Find the integral of sin(ax)

Answer 6

-a cos(ax) +C

Question 7

Find the integral of e^ax

Answer 7

1/a.e^ax +C

Question 8

Find the integral of a/x

Answer 8

a.ln(x) +C

Question 9

What is the formula for gradient?

Answer 9

y=mx+c

Question 10

What is the first rule of differentiation?

Answer 10

Times by power, reduce power by 1

Question 11

What is the first rule of integration?

Answer 11

Increase the power by one, divide by the new power

Question 12

Find the derivative of:

y = 3x^2 - 6cos(x) +2

Answer 12

dy = 6x + 6sin(x)

dx

Question 13

Find the derivative of:

y = ln x - 6e^2x + 1/4x^4

Answer 13

dy = 1/x -12e^2x + x^3

dx

Question 14

Find the gradient of the following:

y = 3x^3 - e^1/2x

When x=1

Answer 14

dy = 9x^2 - 1/2e^1/2x
dx

= 9(1)^2 - 1/2e^1/2(1)

= 9 - e^1/2
2

= 8.18

Question 15

Find the derivative of:

y = 1/2x^2 - 4sin(x) - ln(x)

Answer 15

dy = x - 4cos(x) - 1/x

dx

Question 16

Find the derivative of:

y = e^1/3 + 1/3x^2

Answer 16

dy = 1/3e^1/3x + 2/3x

dx

Question 17

Find the integral of:

y = 1/2x - e^x + cos(1/2x)

Answer 17

fxdx = 1/4x^2 - e^x +2sin(1/2x) +C

Question 18

Find the integral of:

y = 1/x + x^2 - 2sin(3x)

Answer 18

ln(x) + 1/3x^3 + 2/3cos(3x) +C