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Differentiate the following function u = Cos(x3)

u = Cos(x 3 ) To differentiate this function we will use the chain rule. Firstly we will set x 3 to another variable name such as v. So now v = x 3 . Lets differentiate this. dv/dx = 3x 2 We can now differen...
SB
Answered by Serena B. • Maths tutor
4039 Views

Differentiate y = 7(x)^2 + cos(x)sin(x)

This question uses a combination of standard differentiation and the product rule. The second part of the equation cos(x)sin(x) is the product of two funtions so the product rule must be used. Product rule: ...
EC
Answered by Edward C. • Maths tutor
4236 Views

Find the set of values of x for which x(x-4) > 12

When solving this quadratic inequality, we should use a three-step approach. The first step is to reformat the inequality to put one side equal to zero, which is the standard format of a quadratic equation. ...
DB
Answered by Daniel B. • Maths tutor
14749 Views

Simplify (5-2√3)/(√3-1) giving your answer in the form p +q√3, where p and q are rational numbers

The trick here is to use a technique called the difference of squares. If we multiply the top and bottom of the fraction by the conjugate* of the denominator, we can remove any square root terms from the den...
AW
Answered by A W. • Maths tutor
21145 Views

Find the exact solution of the equation in its simplest form: 3^x * e^4x = e^7.

First take natural logs of both sides, giving us: ln(3 x * e 4x ) = ln(e 7 ). The RHS can be simplified using the definition of natural logs, so ln(e 7 ) = 7. We can then apply the product rule for logs (ln(...
HM
Answered by Hugo M. • Maths tutor
5965 Views