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Find dy/dx when y = 5x^6 + 4x*sin(x^2)

Looking at the first element of the equation 5x 6 , we can simply multiply 6 by 5 to give 30 and subtract 1 from the power of x. So d/dx[5x 6 ] = 30x 5 . The next element of the equation is 4x sin(x 2 ), whe...
MJ
Answered by Mark J. • Maths tutor
3446 Views

Simplify ln(e^2) - 4ln(1/e)

Using log rules, we can simplify the equation as follows: Firstly log(x a ) = a log(x) implies that ln(e 2 ) = 2 ln(e). Next log a (a) = 1 implies 2 ln(e) = 2 1 = 2 [Since the natural logarithm ln is equival...
MJ
Answered by Mark J. • Maths tutor
5603 Views

Factorise (5x^2 + 7x + 2)

This expression is in the form of ax^2 + bx + c, so you need to find two numbers which multiply to get ac and add to make b. Step 1: Here a is not = 1, so you need to take out the highest common factor. In t...
DJ
Answered by Daisy J. • Maths tutor
11103 Views

What is the difference between weathering and erosion?

Weathering is the physical or chemical break down of rock or soil in the place where the rock/soil is located - called 'in situ'. No material is transported when an in situ rock is weathered, however its sha...
DJ
Answered by Daisy J. • Geography tutor
11255 Views

Decribe, in terms of electrons ,what happens when a sodium atom reacts with a chlorine atom to form sodium chloride.

This is an example of ionic bonding. The sodium atom loses an electron to become a positive ion . This electron is then gained by the chlorine atom which becomes a negative ion. These two ions then form sodi...
SF
Answered by Seyi F. • Chemistry tutor
13694 Views