1. messy, but correct. I'd have gone on to
(6x^2 + 2x + 3)e^(x^2)
2. almost. Why the "-" sign? d(sinx)/dx = +cosx
e^(sinx) (1/x + lnx cosx)
4. brute force, using the quotient rule:
((2cos 2x)(cosx) - sin 2x (-sinx))/cosx)^2
= (2 cosx cos2x + sinx sin2x)/(cosx)^2
messy. How about simplifying first?
sin2x/cosx = 2sinx cosx / cosx = 2sinx
f' = 2cosx
I'll let you convince yourself that the two are equal
5. Hmmm. I get
f = √x/(3x+1)
f' = ((1/2√x)(3x+1) - √x(3))/(3x+1)^2
= ((3x+1) - 3√x 2√x)/(2√x (3x+1)^2)
= (1-3x)/(2√x (3x+1)^2)
a little algebra mixup in the top?
6. If you mean
f = sin^4(3x+1)-sin(3x+1), just use the good old chain rule on both terms:
f' = 4sin^3(3x+1)(cos(3x+1))(3) - cos(3x+1)(3)
= 3cos(3x+1)(4sin^3(3x+1) - 1)
7. where'd that 2 come from?
1 + y' = -sin(xy)(y+xy')
1 + y' = -ysin(xy) - xsin(xy) y'
y' = -(1+y sin(xy))/(1+x sin(xy))
Dervative of cos(x) is -sin(x) so it would be negative.
tigonometry - expres the following as sums and differences of sines or cosines ...
TRIG! - Posted by hayden on Monday, February 23, 2009 at 4:05pm. sin^6 x + cos^6...
algebra - Can someone please help me do this problem? That would be great! ...
Mathematics - Trigonometric Identities - Let y represent theta Prove: 1 + 1/tan^...
Math - Calculus - The identity below is significant because it relates 3 ...
Precal - Verify the identity: sin^(1/2)x*cosx - sin^(5/2)*cosx = cos^3x sq root ...
Calculus 12th grade (double check my work please) - 1.)Find dy/dx when y= Ln (...
Trig - Given: cos u = 3/5; 0 < u < pi/2 cos v = 5/13; 3pi/2 < v < ...
trig - Reduce the following to the sine or cosine of one angle: (i) sin145*cos75...
Calculus - Consider the function f(x)=sin(1/x) Find a sequence of x-values that ...