Jeopardylabs and Chill

product

100

Differentiate using The product rule H(x)=(x^2)(x^3+4)

=5x^4+8x

200

Differentiate using The product rule z=(4x+9)(8x+5y)

64x + 20y + 72

300

Differentiate using The product rule h(z)= (1 + 2z + 3z^2)(5z + 8z^2 - z^3)

=5 + 36z + 90z^2 + 88z^3 - 15z^4

400

Differentiate using The product rule H(x)=(4x^2-x)(x^3-8x^2+12)

20x^4 - 132x^3 + 24X^2 + 96x - 12

500

Differentiate using The product rule y= (1+sqrt x^3)(x^-3 - (2)(cube rt x))

= -3x^-4 - 3/2(x)^-5/2 - 2/3(x)^-2/3 - 11/3(x)^5/6

Quotient

100

Differentiate using The Quotient rule h(t)= (3t + t^4)/(2t^2 + 1)

(4t^5 + 4t^3 - 6t^2 + 3)/(2t^2 + 1)^2

200

Differentiate using The Quotient rule f(x)=(sqrt(x) + 2x)/(7x - 4x^2)

1/2(x)^1/2 + 2)(7x - 4x^2) - (x^1/2 + 2x)(7 - 8x)/(7x - 4x^2)^2 

300

Differentiate using The Quotient rule f(x)= e^x/x^2

=(e^x(x - 2))/x^3

400

Differentiate using The Quotient rule f(x)= (4x - 2)/(x^2 + 1)

= (-4x^2 + 4x + 4)/(x^2 + 1)^2

Basic

100

derivative of sinx

= cosx

200

derivative of sqrt(x)

1/2sqrt(x)

300

derivative of e^x

=e^x

400

Derivative of cosec(x)= -cosec x cot x

=-cosec(x) cot(x)

500

derivative of x^n

=nx^(n-1)

Chain

100

Differentiate using The chain rule h(x)=(x^2 + 3x  + 1)^2 

= 4x^3 + 18x^2 + 22x + 6

200

Differentiate using The chain rule f(x)= x^4(5x-1)^3

=4x^3(5x-1)^3 + 15x^4(5x-1)^2

300

Differentiate using The chain rule y= 7/(x^2 - 9)^1/2

-7x/(sqrt(x^2 - 9)^3

400

Differentiate using The chain rule h(x)=sin^-1(4x^2)

8x/sqrt(1-16x^4)

Implicit

100

calculate using implicit differentiation x^3 y^3 - y= x

(1 - 3x^(2)y^(3))/(3x^(2)y^(3) - 1)

200

calculate using implicit differentiation 3y^2 + 4y - 3 + 2x= 0

-2x/(3y^2 + 4y - 3)

300

calculate using implicit differentiation y^3=x^2

=2/3(x)^(-1/3)

400

calculate using implicit differentiation y^5 + 2y = x^2

X^ = 2x