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if y= e^(5x) what is dy/dx

For differentiation it is known that d/dx(e^x) = e^x always.This example is slightly more complex as it includes a product of x as the power.In this case we can simplify the question by setting 5x= u therefo...
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Answered by Lucinda D. • Maths tutor
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How do you integrate the term x^2?

When integrating terms that include a power, such as x 2 , there is a simple rule to remember. The rule is to add 1 to the power, and then divide the whole term by this number.For example, in the case, 2 is ...
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Answered by Jack P. • Maths tutor
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Find the partial fraction decomposition of the expression: (4x^2 + x -64)/((x+2)(x-3)(x-4)).

The first step to solving this question is inputting our dummy variables, and laying out the question so we know what we're doing. So we end up with:(4x 2 + x - 64)/((x+2)(x-3)(x-4)) = A /(x+2) + B /(x-3) + ...
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Answered by Matt V. • Maths tutor
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Given f(x): 2x^4 + ax^3 - 6x^2 + 10x - 84, and knowing 3 is a root of f(x), which is the value of a?

For this exercise we need to be aware of the factor theorem.The factor theorem states when f(c) = 0 then x - c is a factor of the polynomial f(x) and c is a root of f(x). Because we are told that one of the ...
SR
Answered by Sabela R. • Maths tutor
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A particle is in equilibrium under the action of four horizontal forces of magnitudes 5 newtons acting vertically upwards ,8 newtons acting 30 degrees from the horizontal towards the left,P newtons acting vertically downwards and Q newtons acting to right

first of all we need the resolve the diagonal force into its horizontal and vertical components. Using trigonometry you can deduce that the horizontal component equates to 8Cos30 and the vertical component e...
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Answered by Ali A. • Maths tutor
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