Differentiation

Which rule

100

To differentiate sin(x²) you will need to use the _______ rule.

Chain

200

To differentiate xe^x which rule(s) would I need?

Product rule

300

To differentiate x/(x^2-4x+8), which rule(s) do i require?

quotient

400

to differentiate e^sin(cos(x))+3x+e^x, how many applications of the chain rule are required?

Two

500

Which rule(s) and how many times are they required to differentiate:

y=sin(cos(x)sin(x)) times sin(xcos(x²))

Chain rule x 3

Product rule x 2

Problem Solving

100

What is the derivative of sin(x²)? 

2xcos(x²)

200

What is the derivative of ln(x²+x-2)?

(2x+1)/(x²+x-2)

300

What is the derivative of cosec(e^x)?

-e^xcosec(e^x)cot(e^x)

400

What is the derivative of 20x³ + 12x² - 7x - 21?

60x² + 24x - 7

500

What is the derivative of:

f(x)=ln(kx)+k³+k²+k+1+x

Fully simplify.

1/x+1

Higher order derivatives

100

Find the third derivative of f(x) = (x²)times(7x)  

42

200

Find the second derivative of f(x)=e^-x

f(x)=e^-x

300

Find the third derivative of:

y=1/x

-6/x⁴

400

What feature of a graph y=f(x) will I find if I solve f''(x)=0

Points of inflection

500

Find the second derivative of f(x)=ln(sin(x))

-csc²(x)

Rules

100

What is the rule for differentiating powers of x?

nx^n-1

or multiply by the power, reduce the power by 1

200

What rule is being used?

f(x )* g’(x) + g(x) * f’(x)

Product Rule

300

What is the name of this rule:

f[g(x)]'=f'[g(x)]g'(x)

Chain rule

400

What type of differentiation do we use when differentiating a pair of equations like:

y=t²+4

x=3t-1

Parametric differentiation

500

Give all the functions that satisfy:

f'(x)=f(x)

f(x)=0

f(x)=e^x

Misc

100

solve for x:

x²(1-x)(1+x)=0

x=0, x=1,x=-1

200

simplify (write as a single log)

 2ln(3x)+ln(x)

ln(9x³)

300

x⁰=1 except for?

x=0

400

Simplify: 2sin(4x)cos(4x)

(write as a single trig function)

sin(8x)

500

Solve (x²)^x+2=1

x=1, x=-1, x=-2