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Find the derivation of (sinx)(e^2x)

Because there are two forms of x , the form uv'+vu' must be used. If y=sinx , dy/dx=cosx If y=e^kx , dy/dx=ke^kx Therefore dy/dx=(sinx)(2e^2x)+(e^2x)(cosx)
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Answered by Eric B. • Maths tutor
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Use logarithms to solve the equation 2^5x = 3^2x+1 , giving the answer correct to 3 significant figures.

Firstly, I would make sure that the student is aware of the basic conept of logarithims and run through the basic "laws" of logarithims to make sure that they have the knowledge they need to answer...
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Answered by Shubhayu G. • Maths tutor
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What are complex and imaginary numbers and how are they different from normal (real) numbers?

When you think of a number line, zero lies at the centre and the positive numbers stretch off to the right, while negative numbers go off left. This is a representation of real numbers, including both ration...
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Answered by Tutor59493 D. • Maths tutor
4072 Views

How do you integrate ln(x) with respect to x?

This integral must be done using integration by parts. Therefore, we set u=ln(x) and dv=dx, which gives du=1/x and v=x. Then, using the integration by parts formula the integral now equals x*ln(x)-int[dx]. T...
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Answered by Oliver H. • Maths tutor
6306 Views

The equation 2x^2 + 2kx + (k + 2) = 0, where k is a constant, has two distinct real roots. Show that k satisfies k^2 – 2k – 4 > 0

Two distinct real roots means that we can use b^2-4ac>0 relationship for any ax^2+bx+c equation. Apply the above gives, 4k^2 - 4 2 (k+2)>0 Simplifying gives, k^2 - 2k -4 >0
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Answered by Andreas T. • Maths tutor
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