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What does derivative mean? The derivative of a function the represents the gradient of the function for each value of x. Remark that the gradient of a function at point (x,f(x)) is equal to the gradient o...

f(x) = 7xe^xUsing the product rule: [f'(x)=u*(dv/dx)+ v*(du/dx)]Let u=7x and v=e^xTherefore, du/dx=7 and dv/dx=e^xHence, f'(x) = 7xe^x + 7e^x

First we should be aware of the relationship bewteen the denominator of the two fractions. Since x^2-9=(x+3)(x-3), we can multiply (x-3) on both numerator and denominator of the fraction of 2/(x+3). Henc...

To find the answer first you have to take a log of both sides.

I am going to use log to the base 2 for my example - but any base will work as long as they are the same on both sides of the equals s...

[would draw diagram to make easier].
We can use Newton's Second Law (F=ma) to resolve the forces acting on each of the blocks (label string on 3kg side T₁ and on 4kg side T₂, an...