Question

differentiate 3^(-x/2)

Answer 1

y=3^(-x/2)
logy=(-x/2)log3
1/y(dy/dx)=-(1/2)log3
dy/dx=y*(-1/2)log3
dy/dx=(3^(-x/2))(-1/2)log3

Answer 2

should be (3^(-x/2))(-x/2)log3

Answer 3

d/dx(Cx^Ax)=Cx^Ax(Aln(Cx)+AxC/Cx)

Answer 4

C=constant, A=constant

Answer 5

d/dx(C^Ax)=C^Ax(Aln(C))

Answer 6

\[f(x)=3^{\frac{x}{2}}=e^{\frac{\ln(3) \times x}{2}}\]
\[f'(x)=\frac{\ln(3)}{2} \times e^{\frac{\ln(3) \times x}{2}}=\frac{\ln(3)}{2} \times 3^{\frac{x}{2}}\]

Answer 7

Umm sorry, forgot the minus symbol, just plug it in and you get
\[f'(x)=- \frac{\ln(3)}{2} \times 3^{- \frac{x}{2}} \]

Answer 8

no, the derivative of C^u is (C^u)(du)(lnC). So, what I did originally, but with ln instead of log. Someone1348's right, too