Differentiate/Integrate Math Help

Hi, im having some problems with the following Differentials

1) y=6 sin 3 theta

2) y= 5e^2^x + 7e^3^x

3) Find the gradient of the curve y = 6x^2 - 6x + 8 where x =3

And the following Integrates

1) y = 3x^4 +6x -7

2) y = 3 cos 6 theta

3) y = 7e^4^x

any help would be of a great advantage

Originally posted by: Swoosh

Hi, im having some problems with the following Differentials

1) y=6 sin 3 theta
dy/d(theta) = 6 * cos(3 theta) * d(3 theta)/d(theta)
= 6 * cos(3 theta) * 3
= 18 cos(3 theta)

3) Find the gradient of the curve y = 6x^2 - 6x + 8 where x =3
dy/dx = 6 * 2x - 6 = 12x - 6
Putting x = 3, dy/dx = 12*3 - 6 = 36 - 6 = 30
Ans: 30

And the following Integrates

1) y = 3x^4 +6x -7
Integral y dx = 3 x^5 /5 + 6 x^2 /2 - 7x + C
= 3/5 * x^5 + 3 x^2 - 7x + C, where C is the constant of integration

2) y = 3 cos 6 theta
Integral y dtheta = 3 sin(6 theta)/6 + C = 1/2 * sin(6 theta) + C, where C is the constant of integration

Two problems left. Will do after some time.