AP Calc AB Final Project: Surinder Bath

Trig Functions

100

Find the first derivative of the function.

f(x)=sin3x+8cos2x

3cos3x-16sin2x

200

Find the first derivative of the function:

f(x)=2cos(5x³+2x²+1)

-2sin(5x³+2x²+1)(15x²+4x)

300

What is the first derivative of this function:

f(x)=(sin8x²)(cot2x)

16xcos(8x²)cot(2x)-2csc²(2x)sin(8x²)

400

What is the first derivative of the function:

f(x)=2(cos(8x³+2))³

-144x²cos²(8x³+2)sin(8x³+2)

500

What is the first derivative of the function:

f(x)=(sin(9x⁴+2x)/(cot(3x))

(cos(9x⁴+2x)cot(3x)(36x³+2)+3csc²(3x)sin(9x⁴+2x))/cot²(3x)

Log Functions

100

Find the first derivative of the function:

f(x)=ln(3x²+5x)

(6x+5)/(3x²+5x)

200

Find the first derivative of the function:

f(x)=log₂(7x⁵+3x²+8)

(35x⁴+6x)/((ln2)(7x⁵+3x²+8))

300

Find the first derivative of the function:

f(x)=(3x)(ln(8x³+2))

3[ln(8x³+2)+(12x³)/(4x³+1)]

400

Find the second derivative of the function:

f(x)=ln(3x²+1)

6(1-3x²)/(3x²+1)²

500

Find the first derivative of the function:

f(x)=(log₃(8x²+1))(ln2x)

(16xln(2x)/(ln3)(8x²+1))+(log₃(8x²+1)/x)

Exponential Functions

100

Find the first derivative of the function:

f(x)=e^{3x^5}+2

f'(x)=15x⁴e^{3x^5}

200

Find the first derivative of the function:

f(x)=e^2x(3x⁴+8x)

2e^2x(3x⁴+8x)+e^2x(12x³+8)

300

Find the first derivative of the function:

f(x)=(e^{3x^2})/(e^6x)

e^{(3x^2)-6x}(6x-6)

400

Find the first derivative of the function:

f(x)=2^{8x^4}

ln(2)2​⁽​​​^{8x^4)+5}x³

500

Find the first derivative of the function:

f(x)=(2^3x)/(8^3x)

-6ln(2)(1/4)^3x

Polynomial Functions

100

The first derivative of this function:

f(x)=3x³+5x²+8

f'(x)=9x²+10x

200

What is the first derivative of this function?

f(x)=(2x+3)(5x²)

30x²+30x

300

What is the first derivative of this function?

f(x)=3(9x+2)²

54(9x+2)

400

What is the first derivative of this function?

f(x)=(3x²+8x)/(4x³+2)

-(3x⁴+16x³-3x-4)/(2x³+1)²

500

What is the first derivative of this function?

f(x)=3(5x²+8x)²(3x+4)

f'(x)=3(375x⁴+1360x³+1536x²+512x)