Find the gradient of  $ \displaystyle ax^b+\frac{c}{x^{d}}+f$ at $x=n$

An introduction to using the quotient rule

Finding the stationary points of a cubic with two turning points

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A basic introduction to differentiation

Using the chain rule with polynomials and negative powers

Introduction to using the product rule

Using the chain rule within product rule problems

An introduction to using the quotient rule

Find the gradient of  $ \displaystyle ax^b+\frac{c}{x^{d}}+f$ at $x=n$

A basic introduction to differentiation

Identifying the correct rule to use

More work on differentiation with fractional coefficients

More work on differentiation with fractional coefficients and powers

More work on differentiation with fractional coefficients.

Differentiation of trigonometric functions

Using the chain rule with polynomials

Differentiating the natural logarithm

Differentiating further exponentials

Real life problems with differentiation

More work on differentiation with trigonometric functions

Differentiating exponentials

Application of differentitaion in geology. A projectile problem.

A portfolio of NUMBAS questions created for first year Natural Sciences students. The questions cover the topics: 

• Linear functions
• Quadratic functions
• Differentiation
• Integration
• Explonatial and logarithms 
• Further differentiation
• Further Integration
• Trigonometric Functions

Calculating the rate of change of the temperature during a chemical reaction using the chain rule in a function of the form $T=ate^{-t}$, and finding the maximum temperature of the reaction.

Using basic derivatives to calculate the gradient function of a hill $y=-e^{x}+b\ln{\left(x\right)+c$, and then substituting values to find the gradient at specific distance from the sea. 

Finding the stationary point (maximum) of a quadratic equation in a contextualised problem. 

Calculating the gradient of a quadratic equation at a specific point and finding the stationary point (maximum) in a contextualised problem. 

Calculating the derivative of a function of the form $a \ln(bx)$ using a table of derivatives.

Partial differentiation question with customised feedback to catch some common errors.