[SOLVED] Chain rule with functions depending on other functions

Hello all! I'm stuck in a big way on this one.

Here are the givens:

q1(P,S,y) = 6*P^(-2)*S^(3/2)*y

q2(P,S,y) = 4*P*S^(-1)*y^2

P(t) = (12*t)^(1/2)

S(r,t) = 10*r*t^2

y(r) = 20r.

Find the derivative of q1 and q2 with respect to both time t and interest rate r when t=3 and r=0.1.

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Here's my methodology:

partial q1/partial t = partial q1/partial P*dP/dt + partial q1/partial S*partial S/partial t + partial q1/partial y*dy/dt

partial q1/partial r = partial q1/partial P*dP/dr + partial q1/partial S*partial S/partial r + partial q1/partial y*dy/dr

partial q2/partial t = partial q2/partial P*dP/dt + partial q2/partial S*partial S/partial t + partial q2/partial y*dy/dt

partial q2/partial r = partial q2/partial P*dP/dr + partial q2/partial S* partial S/partial r + partial q2/partial y*dy/dr

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Getting started on the calculations, I plugged in (P=6, S=9, y=2) to the partials of q1 and q2:

partial q1/partial P = -12*P^(-3)*S^(3/2)*y = -3

partial q1/partial S = 9*P^(-2)*S^(1/2)*y = 1.5

partial q1/partial y = 6*P^(-2)*S^(3/2) = 4.5

partial q2/partial P = 4*S^(-1)*y^2 = 16/9

partial q2/partial S = -4*P*S^(-2)*y^2 = -32/27

partial q2/partial y = 8*P*S^(-1)*y = 32/3

Putting those numbers into a matrix:

Row 1 (q1): -3 1.5 4.5

Row 2 (q2): 16/9 -32/27 32/3

Then putting the derivatives of the functions upon which the first functions depend, evaluated at t=3 and r=0.1 into a matrix (the derivative wrt t is in the first column, and the derivative wrt r is in the second column):

Row1: 1 0

Row 2: 6 90

Row 3: 0 20

Multiplying my two matrices together, I get:

Row 1: 6 225

Row 2: -5.33 106.66

But none of those numbers are correct (unless there is a mistake in the text I am using). Can someone please point out where I'm going wrong?

Thanks and all the best!