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Solving harder exponential equations, e.g. 5/[exp(x) + 6exp(-x)] - 1 = 0 . CORE MATHS.

Our example equation is, 5/[exp(x) + 6exp(-x)] - 1 = 0 ,and we wish to solve for x. Note that exp(x) is the same as writing e^xI have chosen this one, because it helps illustrate some general g...

Answered by Matthew S. • Maths tutor

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How do I differentiate (cosx)/x^2

Label function: y=(cosx)/x²Recall quotient rule for functions of form h(x)=f(x)/g(x) given by,h'(x)=(f'(x)g(x)-f(x)g'(x))/(g(x))²Split original equation into f(x)=cosx and g(x)=x

Answered by Caelen D. • Maths tutor

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You are given the equation of the line y=x^3+x^2-2x. Find the stationary points of the curve and determine the maximum and minimum points and find where it crosses the x-axis and thus sketch the graph

First differentiate the equation to find the equation of the tangents in terms of x. From this set dy/dx=0 because this is the stationary points, from this use the quadratic equation to find the value of ...

Answered by Oliver H. • Maths tutor

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Integrate $$\int xe^x \mathop{\mathrm{d}x}$$.

We use integration by parts. Set $u = x$ and $dv/dx = e^x$. This leads to $du/dx = 1$, and $v = e^x$. Then:\begin{align*}\int xe^x \mathop{\mathrm{d}x} &= xe^x - \int e^x \mathop{\mathrm{d}x}\&= x...

Answered by Christopher N. • Maths tutor

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Where does the quadratic formula come from?

This is one of the most common a level math question. One which is essential to understand as it gives a firm understanding of core fundamental principles in math which are Completing the square and Algeb...

Answered by Riyadh M. • Maths tutor

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