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how can differentiate using the product and chain rule? e.g y=(4x+1)^3(sin2x), find dy/dx.

First you have to identify the equation for y is a product. Then you can apply the product rule using (4x+1)^3 as one term and sin2x as the other. First you differentiate (4x+1)^3 using the chain rule. You d...
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Answered by Rajvir J. • Maths tutor
4988 Views

The curve C has the equation: 2(x^2)y + 2x + 4y – cos (πy) = 17 use implicit differentiation to find dy/dx in terms of x and y

Using the product rule: d/dx(ab)=ab’ + a’b where a and b are variables which have been differentiated with respect to x Derivative: 2(x^2(dy/dx)+2xy) + 2 + 4dy/dx+πsin(πy)dy/dx=0 Expand brackets: 2x^2(dy/dx)...
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Answered by George G. • Maths tutor
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Solve the following inequality and shade the region to which it applies on a graph. 10x(squared) < 64x - 24

Step 1: Simplify the quadratic by dividing by 2. 5x 2 &lt; 32x - 12 Step 2: Move all terms onto one side of the quadratic. 5x 2 - 32x + 12 &lt; 0 Step 3: Factorise the quadratic. (5x - 2)(x - 6) &lt; 0 Step ...
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Answered by Thomas S. • Maths tutor
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June 2008 C1 Paper Differentiation Question

a) ask student: purpose of differentiation (i), how to perform differentiation (ii) (i) to find the gradient of a curve (ii) multiply the coefficient of x by its indice then minus one from the indici perform...
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Answered by Nicola G. • Maths tutor
3502 Views

Find the exact solution, in its simplest form, to the equation 2ln(2x+1) - 10 = 0.

We want to &quot;undo&quot; every step of the equation until we have just x on one side. So first add 10 to each side and then divide both sides by 2 to give ln(2x+1) = 5. Take the exponential of each side t...
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Answered by Eleanor B. • Maths tutor
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