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Use implicit differentiation to find dy/dx of: 2(x^2)y + 2x + 4y - cos((pi)y) = 17

Tackle this problem one part at a time: First differentiate 2x²y using the product rule, showing dy/dx(2x²y) = 4xy + 2x²(dy/dx). After this, the remainder of the question ...

Answered by Nick E. • Maths tutor

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Why don't I have to put the +C after my answer for a definite integral?

When you evaluate a definite integral, we can think about using the "+C" and see what happens. Let's take (INT)2x dx between 2 and 3. We then have [x²+C] between 2 and 3. For x=3 we h...

Answered by Joseph C. • Maths tutor

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Integrate 1 / x(2sqrt(x)-1) on [1,9] using x = u^2 (u > 0).

Differentiate x = u²to get dx = 2u du. We need to change the limits, too:

1 <= x <= 9 <==> 1 <= u² <= 9 <==> 1 <= u <= 3 (since we are give...

Answered by Tutor69809 D. • Maths tutor

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Show that, for all a, b and c, a^log_b (c) = c^log_b (a).

We want to prove:

a^log_b(c) = c^log_b(a).

Recall that we can always write x = e^ln(x), so x^y = (e^ln(x))^y

Answered by Tutor69809 D. • Maths tutor

6151 Views

Use the substitution u=3+(x+4)^1/2 to find the integral of 1/(3+(x+4)^1/2) dx between 0 and 5.

We will call the integral I, so I = integral of 1/(3+(x+4)^1/2) dx between 0 and 5. First substitute u=3+(x+4)^1/2 into the equation to get I = integral of 1/u dx between 0 and 5 Next ...

Answered by Calum B. • Maths tutor

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