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Show that the derivative of tan(x) is sec^2(x), where sec(x) is defined as 1/cos(x). [Hint: think of tan(x) as a quotient of two related functions and apply the appropriate identity]

tan(x) is defined as sin(x)/cos(x) For a function which can be written as f(x) = u(x)/v(x) the quotient rule can be appliedThe quotient rule states f ' (x) = (u'v-v'u)/v^2 Applying this to the formula for...

Answered by Oliver C. • Maths tutor

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Given that dy/dx = 6x*2 - 3x + 4 And y =14 when x=2. Express y in terms of x

Dy/dx = 6x²- 3x + 4y = 12x - 3 + c14 = 12(2) - 3 + (c)14= 24 - 3 + c14 = 21 + cc= -7y = 12x - 10

Answered by Medi N. • Maths tutor

2183 Views

Integrate y= x^3+3x^2-4x-7 between x values 1 and 3

Firstly, integrate y with respect to dx. Increase the powers of x by 1 and then divide the coefficient of x by the new power of x. I.e.: x^3 becomes 1/4x^4. The power increases from 3 to 4 and the coeffic...

Answered by Louis A. • Maths tutor

2881 Views

Given the functions f(x) = (x + 2)/9 and g(x) = x^3 + 6, find fg(x).

Firstly, fg(x) could be written as f[g(x)], or in other words, the function f acts on the result of x going through the function g (Bear in m...

Answered by Josh J. • Maths tutor

4530 Views

What is proof and how does it work?

'Proving' something mathematically means showing that it is true for all possible cases. Therefore it isn't sufficient to simply give a lot of examples of a formula or test working; you need to find a way...

Answered by Cameron B. • Maths tutor

3240 Views