Differentiation of inverse hyperbolic functions

Revision Points - Differentiation of Inverse Hyperbolic Functions

Definition and Basic Knowledge

• Inverse hyperbolic functions reverse the actions of hyperbolic functions.
• They make an angle’s hyperbola match a number. They are represented by sinh^-1(x), cosh^-1(x) and tanh^-1(x).

Understanding Differentiation

• The process of finding a function’s derivative is known as differentiation.
• Differentiation allows you to find the slope or rate of change at any point in a function.

Formulas for Differentiating Inverse Hyperbolic Functions

• You should know and understand the derivatives for each inverse hyperbolic function.
• The derivative of sinh^-1(x) is 1/sqrt(x²+1).
• The derivative of cosh^-1(x) is 1/sqrt(x²-1).
• The derivative of tanh^-1(x) is 1/(1-x²).

Applying Differentiation

• Use the formulas to determine the slope of the tangent line to the curve at a certain point.
• When differentiating more complicated functions that include sinh^-1(x), cosh^-1(x) or tanh^-1(x), use the chain rule.
• Your ability to differentiate effectively is crucial in many areas of Core Pure Maths, including additional differentiation and integration topics.

Context and Practice

• Review how these differentiation formulas are used in real-world scenarios, such as solving physics or engineering problems.
• Gain a better understanding by using these formulas to solve problems.
• Familiarise yourself with these concepts by practising regularly with a range of different problems.

Remember, mastering inverse hyperbolic functions and their differentiation is crucial for performing well in Core Pure Maths. Always keep practicing and strive to understand each step taken during differentiation.