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how to derive escape velocity

escape volocity is the minimum volocity required for one object toescape the gravitationl feild of another.we find this by equating gravitional potental enegy and the kinetic energy of the object to 1/2 *...

Answered by Aidan M. • Maths tutor

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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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