Calculus Test

Calculate 3pi/4 and pi (sec^2tdt)

-1

Differentiate y=ln(cos 2x)

-2 sin 2x/cos 2x

Differentiate y=ln(cos 4x)

-4 sin 4x/cos 4x

Find indefinite integral (-5 cos x+4 sin x) dx

-5 sin x-4 cos x+C

Differentiate y=-9 sin t with respect to t:

-9 cos t

Find indefinite integral (-9 cos x+2 sin x) dx

-9 sin x-2 cos x+C

Differentiate y=-3(sin^2x+cos^2x) with respect to x:

0

Differentiate y=7(sin^2x+cos^2x) with respect to x:

0

Find indefinite integral cos 3x dx:

1/3 sin(3x)+C

Find indefinite integral cos 3xdx

1/3 sin(3x)+C

Find indefinite integral cos 7x dx:

1/7 sin(7x)+C

Differentiate f(x)=11 tan(x^2+x+9) with respect to x

11(2x+1)sec^2(x^2+x+9)

Find area under curve y=cos t from t=pi/3 to t=pi/2

2-square root of 3/2

Evaluate pi/36 and -pi/36 (sec^2 9xdx)

2/9

Differentiate y=tan square root of 8x

4 sec^2 square root of 8x/square root of 8x

Find area under curve y=cos t from t=pi/5 to t=pi/4

4-square root of 5/4

Calculate pi/8 and 0 (5sec^2t dt)

5

Calculate pi/4 and 0 (7sec^2t dt)

7

Differentiate f(x)=7 tan (x^2+x+5) with respect to x

7(2x+1)sec^2(x^2+x+5)

Differentiate y=square root of sin(x+2) with respect to x:

cos (x+2)/2square root of sin(x+2)

Differentiate y=square root of sin(x-6) with respect to x:

cos (x-6)/2square root of sin(x-6)

Differentiate y=sin t with respect to t:

cos t

Differentiate y= ln(2 tan t)

csc t sec t

Evaluate 1/cos^2xdx

tan(x)+C