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differentiate x^2 + 7x + 4

To differentiate you must times by the power then take one away from the power. Therefore x^2 + 7x + 4 would differentiate to become 2x + 7. The generic rule for differentiation can be written as dy/dx (x n ...
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Answered by Ajay D. • Maths tutor
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How can do you factorize the equation x^2+6x+8

Here, we see that the term in x in the equation is 6, so we start by looking for a perfect square where the second term would be 6 : we get 6/2 = 3 so we try (x+3) 2. However, (x+3) 2 = x 2+ 6x + 9. We thus ...
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Answered by Marine S. • Maths tutor
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Differentiate with respect to x, x^2*e^(tan(x))

Use the product rule: d/dx(uv) = uv' + u'v, with u = x^2 and v = e^(tan(x)), so that u' = 2x and v' = sec^2(x) * e^(tan(x)), and so the answer is 2x * e^(tan(x)) + x^2 * sec^2(x) * e^(tan(x)) .
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Answered by Jakub H. • Maths tutor
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Using partial fractions, find f(x) if f'(x)=5/(2x-1)(x-3)

First step: partial fractions 5/(2x-1)(x-3) 5=A(x-3)+B(2x-1) A=0 when x=3, so B=5/(2x3-1)=1 B=0 when x=1/2, so A=5/(0.5-3)=-2 So f'(x)=1/(x-3)-2/(2x-1) Second step: Integration f(x)= (integral)(1/(x-3))dx - ...
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Answered by Jasmin F. • Maths tutor
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When Integrating by parts, how do you know which part to make "u" and "dv/dx"?

you need to think about how the integral will be simpliefied, basically you are trying to get to a state where only one function of x resides in the integral. so if you have an x 2 sin3x dx inside the integr...
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Answered by Thomas G. • Maths tutor
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