CadyMath

#1. \(g\left(x\right)=\frac{1}{x^{4}}\)

\(g^\prime\left(x\right)=\frac{-4}{x^{5}}\)

\(g^\prime\left(x\right)=\frac{-8}{x^{5}}\)

\(g^\prime\left(x\right)=\frac{2}{x^{4}}\)

\(g^\prime\left(x\right)=\frac{8}{x^{5}}\)

#2. \(h\left(y\right)=-e^{y}\)

\(h^\prime\left(y\right)=-3e^{y}\)

\(h^\prime\left(y\right)=-e^{y}\)

\(h^\prime\left(y\right)=3e^{y}\)

\(h^\prime\left(y\right)=e^{y}\)

#3. \(h\left(y\right)=2\ln\left(y\right)\)

\(h^\prime\left(y\right)=\frac{-3}{y}\)

\(h^\prime\left(y\right)=\frac{-5}{y}\)

\(h^\prime\left(y\right)=\frac{2}{y}\)

\(h^\prime\left(y\right)=\ln\left(y\right)\)

#4. \(f\left(y\right)=-4\ln\left(y\right)\)

\(f^\prime\left(y\right)=-\ln\left(y\right)\)

\(f^\prime\left(y\right)=\frac{-2}{y}\)

\(f^\prime\left(y\right)=\frac{-3}{y}\)

\(f^\prime\left(y\right)=\frac{-4}{y}\)

#5. \(f\left(x\right)=2x^4-9x^3+14x^2-9x+2\)

\(f^\prime\left(x\right) =4e^{x-6}\)

\(f^\prime\left(x\right) =\frac{1}{\sqrt{2x-1}}\)

\(f^\prime\left(x\right)=-8x^3+27x^2-28x+9\)

\(f^\prime\left(x\right)=8x^3-27x^2+28x-9\)

#6. \(f\left(y\right)=\sqrt{2y-3}\)

\(f^\prime\left(y\right) =2\csc\left(-y-2\right)\cot\left(-y-2\right)\)

\(f^\prime\left(y\right) =2\sin\left(-2y-3\right)\)

\(f^\prime\left(y\right)=\frac{-\frac{1}{2}}{\sqrt{2y-3}}\)

\(f^\prime\left(y\right)=\frac{1}{\sqrt{2y-3}}\)

#7. \(h\left(x\right)=2e^{-5x+4}+4\)

\(h^\prime\left(x\right) =-1.099\cdot 3^{x-4}\)

\(h^\prime\left(x\right) =6\sin\left(-3x+2\right)\)

\(h^\prime\left(x\right) =\frac{-1}{\sqrt{-2x-2}}\)

\(h^\prime\left(x\right)=-10e^{-5x+4}\)

#8. \(h\left(t\right)=\sqrt{-t+4}\)

\(h^\prime\left(t\right) =-4\cos\left(-2t-2\right)\)

\(h^\prime\left(t\right) =3t^2+6t+1\)

\(h^\prime\left(t\right)=\frac{-\frac{1}{2}}{\sqrt{-t+4}}\)

\(h^\prime\left(t\right)=\frac{-\frac{1}{4}}{\sqrt{-t+4}}\)

#9. \(g\left(y\right)=e^{y+5}\)

\(g^{\prime\prime}\left(y\right) =-0.971\cdot 5^{y-5}\)

\(g^{\prime\prime}\left(y\right) =42y-16\)

\(g^{\prime\prime}\left(y\right)=-\frac{1}{2}e^{y+5}\)

\(g^{\prime\prime}\left(y\right)=e^{y+5}\)

#10. \(h\left(t\right)=-1\)

\(h^{\prime\prime}\left(t\right) =1920t^2+744t-328\)

\(h^{\prime\prime}\left(t\right) =\frac{-1}{-2t-5^{1.5}}\)

\(h^{\prime\prime}\left(t\right) =\frac{-\frac{1}{4}}{t+1^{1.5}}\)

\(h^{\prime\prime}\left(t\right)=0\)