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Differentiate sin(5x) and 3cos(x) and 3tan(5x)

sin cos -sin -cos (down is differentiate and up is integrate) so, y = sin5x dy/dx = 5cos5x y=3cox dy/dx = -3sinx y=3tan5x dy/dx = 15sec 2 (5x) (remember sec(x) is the reciprocal of cos(x))
AC
Answered by Abi C. • Maths tutor
5288 Views

Find where the curve 2x^2 + xy + y^2 = 14 has stationary points

d/dx (xy) = x dy/dx + y d/dx (y^2) = 2y dy/dx [This is from the chain rule] So, d/dx (2x^2 + xy + y^2 = 14) => 4x + x dy/dx + y + 2y dy/dx = 0 set dy/dx = 0 as stationary point has gradient 0 Obtains 4x+y...
MH
Answered by Matthew H. • Maths tutor
9169 Views

Using complex numbers, derive the trigonometric identities for cos(2θ) and sin(2θ).

When dealing with complex numbers and trigonometric functions, always turn to DeMoivre's Theorem that states [cos(θ)+isin(θ)] n = [cos(nθ)+ i sin(nθ)]. If we set n=2, the we see a combination of cos(2θ) and ...
TK
Answered by Thomas K. • Maths tutor
9555 Views

Integrate (x+3)^(1/2) .dx

[whiteboard feature does not seam to be working here] Here we need to make a U sibstitution. So we take (x+3) and make this equal U so we now have the integral of u^1/2 . dx In order to switch to .du and do ...
CZ
Answered by Callum Z. • Maths tutor
5215 Views

Use implicit differentiation to find the derivative of 2yx^2, with respect to x.

To solve this question we use the product rule, where we differentiate one variable whilst keeping the other constant, and vice versa, adding the two results together to get our answer. A helpful formula is ...
DW
Answered by Daniel W. • Maths tutor
9270 Views