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differentiate y=e^2x

y=e^x When we derive, the power is brought down to the front - e.g. 2e^2x. Once this has been reached, you must normally remember to reduce the power by 1. However, with the exponentials, the power remains t...
JJ
Answered by Jamie J. • Maths tutor
18549 Views

Find the set of values for x for which x^2 - 9x <= 36

Rearrange to get x^2 - 9x - 36 &lt;= 0 Solve quadratic (x-12)(x+3) &lt;= 0 Solve for x x = 12, x = -3 Now, we have key points 12 and -3, we need the range of values for x where x^2 - 9x - 36 &lt;= 0. So, we ...
DD
Answered by Daniel D. • Maths tutor
11674 Views

Why does d/dx (tan(x)) = sec^2(x)?

This result comes from using a trig identity and the quotient rule. First, we write tan(x) as sin(x)/cos(x). Then we apply the quotient rule. After doing the standard derivatives, the numerator of our fracti...
TD
Answered by Tutor42661 D. • Maths tutor
12754 Views

Find dy/dx of the equation (x^3)*(y)+7x = y^3 + (2x)^2 +1 at point (1,1)

Use the product rule d(u.v)/dx = u.(dv/dx) + v(du/dx). Calculate the LHS as such first. (Demonstrate on whiteboard.) Then calculate the RHS. (Demonstrate on whiteboard.) Group the dy/dx terms on one side of ...
SP
Answered by Sophie P. • Maths tutor
6013 Views

The curve C is defined by x^3 – (4x^2 )y = 2y^3 – 3x – 2. Find the value of dy/dx at the point (3, 1).

When we find dy/dx we find the gradient of the curve at (3,1). Start by differentiating the left hand side (LHS) like so.. (whiteboard). Remember every time we differentiate a y value we multiply by dy/dx. T...
CR
Answered by Caitlin R. • Maths tutor
5692 Views