 Oct 2021

activecalculus.org activecalculus.org

6. Find the differential of the function w=x3sin(y5z1) dw=dx+ dy+
For this all we do is take the derivative of the function w with respect to x, y and z. we should also recognize that this is a chain rule for y and z. so the chain rule is d/dx f(g(x)) = f(g(x))(g'(x))
with respect to x: 3x^2 sin(y^5 z) dx
with respect to y: 5(x^3 y^4 z) sin(y^5 z) dy
with respect to z: x^3 y^5 sin(y^5 z) dz
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activecalculus.org activecalculus.org

Let z=g(u,v) and .u(r,s),v(r,s). How many terms are there in the expression for ?∂z/∂r? terms Answer. \(2\) 2
For the chain rule we know the formula multiplies the partial derivative with respect to a variable with the derivative of the given variable= values. so, since g(u,v) has only the two values of u and v we can conclude that there are only two expressions for this chain rule.
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 Aug 2018

www.ncbi.nlm.nih.gov www.ncbi.nlm.nih.gov

CONCLUSIONS: These findings suggest that higher standing BP is a biomarker that helps identify persons with combat PTSD who are likely to benefit from prazosin. These results also are consistent with α1AR activation contributing to PTSD pathophysiology in a subgroup of patients.
This is precisely the results I would expect. However, I completely disagree with their interpretation.
People with high blood pressure (BP) can tolerate a reduction in BP without instigating compensatory mechanisms. People with normal or low BP would invoke compensation by the sympathetic nervous system in response to alpha blockade. This would counteract the depressant effects of adrenergic antagonism. Indeed, adrenaline and noradrenaline elevate in response to standing, which I find to be an obvious prediction. Thus, the lack of benefit from prazosin in these subjects may be mediated by an increase in adrenergic receptor activation other than the apha1adrenoreceptor; in particular, the betaadrenergic receptors are likely at fault. Propranolol, a betablocker, is used for PTSD, so this mechanism seems well substantiated.
The study apparently found benefit for patients with BP over 110 (with more benefit for higher BP). Thus, I would conclude that systolic pressure below 110 induce compensation.
