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Differentiate the following equation with respect to x; sinx + 3x^2 - 2.

The first step with any differentiation question is to identify which variable you are differentiating with respect to. In this case the variable is x, so we know we're looking to differentiate each term inv...
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Answered by Ross A. • Maths tutor
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What is the derivative of y=(e^(2x))(sin(3x))

This question is slightly complex and requires you to use multiple differentiation rules. Since we are differentiating a product of two functions, the first rule that we have to use is the product rule: mult...
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Answered by Sajidah H. • Maths tutor
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Differentiate y= exp(cos^2(x)+sin^2(x)) by using the chain rule.

First of all instead ,we'll define the chain rule , thus y can be rewritten as y = f (g(x)) , where f(x) = exp (x) and g(x) = cos^2(x) + sin^2(x). Therefore let y = f(u) , dy/dx = dy/du * du/dx , which then ...
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Answered by Ayman J. • Maths tutor
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The point P lies on a curve with equation: x=(4y-sin2y)^2. (i) Given P has coordinates (x, pi/2) find x. (ii) The tangent to the curve at P cuts the y-axis at the point A. Use calculus to find the coordinates of the point A.

To find the x coordinate of point P, we simply substitute in the value of y at P into the equation of the curve and solve for x = 4pi^2. (ii) To start, we can differentiate x with respect to y, by using the ...
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Answered by Tobias F. • Maths tutor
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The point P lies on the curve C: y=f(x) where f(x)=x^3-2x^2+6x-12 and has x coordinate 1. Find the equation of the line normal to C which passes through P.

First we must find the y coordinate of the point P: We know the x-coordinate is x1=1 so the y coordinate must satisfy the equation y1=f(1) which gives y1=-7. So we now know P is at (1,-7). We now need to fin...
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Answered by Kieran H. • Maths tutor
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