Chain Rule

Polynomials

100

Find the derivative of...

y=x⁴+24x²+4^1/2

What is y'=4x³+48x

200

Find the derivative of...

d/dx (6x)²

What is 72x

300

Find the derivative of...

y=(x³+x²)³

What is y'=3(x³+x²)²(3x²+2x)

400

Find the derivative of...

d/dx (2x⁴+4x²)^1/2

What is (1/2)(2x⁴+4x²)^-1/2(8x³+8x)

500

Find the derivative of...

d/dx (3x⁵+4x³-7x²+12x)^2/3

What is (2/3)(3x⁵+4x³-7x²+12x)^-1/3(15x²+12x²-14x+12)

Trig (Angles)

100

Find the derivative of...

d/dx tan(3x)

What is 3sec²(3x)

200

Find the derivative of...

d/dx sin(3x²)

What is 6xcos(3x²)

300

Find the derivative of...

d/dx cot(x⁴)

What is -4x³csc²(x⁴)

400

Find the derivative of...

d/dx 4cos(x²)

What is -8xsin(x²)

500

Find the derivative of...

d/dx csc(2x⁴)

What is -8x³csc(2x⁴)cot(2x⁴)

Trig (Powers)

100

Find the derivative of...

y=(tanx)²

What is y'=2sec²(x)tan(x)

200

Find the derivative of...

d/dx (2secx)⁵

What is 5[2sec(x)]⁴[2sec(x)tan(x)]

300

Find the derivative of...

y=(sinx)²+(cosx)²

What is y'=2(sinx)(cosx)-2(cosx)(sinx)

= 2[(1/2)sin(2x)]-2[(1/2)sin(2x)]

=0

400

Find the derivative of...

y=[45x+sin(x)]³

What is y'=3[45x+sin(x)]²[45+cos(x)]

500

Find the derivative of...

y=[sec(x)]⁴+[csc(x)]⁴

What is y'=4sec⁴(x)tan(x)-4csc⁴(x)cot(x)

Challenge Round

100

Find the derivative of...

d/dx sin(2x)+cos(3x)

What is 2cos(2x)-3sin(3x)

300

Find the derivative of...

d/dx (7x)²+8y²-(9cosx)²

What is 98x+2(9cosx)(9sinx)

400

Find the derivative of...

d/dx (sin²x+cos²x)²

What is 1