CadyMath

#1. \(f\left(x\right)=3e^{x}\)

\(f^\prime\left(x\right)=-2e^{x}\)

\(f^\prime\left(x\right)=-3e^{x}\)

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

\(f^\prime\left(x\right)=3e^{x}\)

#2. \(h\left(t\right)=\frac{-6}{t^{3}}\)

\(h^\prime\left(t\right)=\frac{15}{t^{4}}\)

\(h^\prime\left(t\right)=\frac{18}{t^{4}}\)

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

\(h^\prime\left(t\right)=\frac{9}{t^{4}}\)

#3. \(h\left(z\right)=-e^{z}\)

\(h^\prime\left(z\right)=-6e^{z}\)

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

\(h^\prime\left(z\right)=2e^{z}\)

\(h^\prime\left(z\right)=6e^{z}\)

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

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

\(g^\prime\left(x\right)=\frac{-3}{x}\)

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

\(g^\prime\left(x\right)=\frac{1}{x^{2}}\)

#5. \(g\left(t\right)=\frac{1}{t}\)

\(g^\prime\left(t\right)=\frac{-1}{t^{2}}\)

\(g^\prime\left(t\right)=\frac{-1}{t}\)

\(g^\prime\left(t\right)=\frac{-5}{t^{2}}\)

\(g^\prime\left(t\right)=\frac{1}{t^{2}}\)

#6. \(g\left(y\right)=\ln\left(y\right)\)

\(g^\prime\left(y\right)=\frac{-1}{y}\)

\(g^\prime\left(y\right)=\frac{1}{y}\)

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

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

#7. \(g\left(y\right)=-6\ln\left(y\right)\)

\(g^\prime\left(y\right)=-2\ln\left(y\right)\)

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

\(g^\prime\left(y\right)=2\ln\left(y\right)\)

\(g^\prime\left(y\right)=\frac{-6}{y}\)

#8. \(s\left(y\right)=-6e^{y}\)

\(s^\prime\left(y\right)=-2e^{y}\)

\(s^\prime\left(y\right)=-6e^{y}\)

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

\(s^\prime\left(y\right)=6e^{y}\)

#9. \(g\left(t\right)=-5\sin\left(t\right)\)

\(g^\prime\left(t\right)=-5\cos\left(t\right)\)

\(g^\prime\left(t\right)=2\sin\left(t\right)\)

\(g^\prime\left(t\right)=4\sin\left(t\right)\)

\(g^\prime\left(t\right)=\cos\left(t\right)\)

#10. \(h\left(t\right)=-2\ln\left(t\right)\)

\(h^\prime\left(t\right)=-\ln\left(t\right)\)

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

\(h^\prime\left(t\right)=\frac{1}{t}\)

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

#11. \(h\left(z\right)=2\ln\left(z\right)\)

\(h^\prime\left(z\right)=-6\ln\left(z\right)\)

\(h^\prime\left(z\right)=3\ln\left(z\right)\)

\(h^\prime\left(z\right)=\frac{1}{z}\)

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

#12. \(h\left(t\right)=2\ln\left(t\right)\)

\(h^\prime\left(t\right)=5\ln\left(t\right)\)

\(h^\prime\left(t\right)=\frac{1}{t}\)

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

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

#13. \(s\left(z\right)=-4\cdot 6^{z}\)

\(s^\prime\left(z\right)=-3\cdot 6^{z}\)

\(s^\prime\left(z\right)=-7.167\cdot 6^{z}\)

\(s^\prime\left(z\right)=3\cdot 6^{z}\)

\(s^\prime\left(z\right)=5.375\cdot 6^{z}\)

#14. \(f\left(y\right)=2\cdot 2^{y}\)

\(f^\prime\left(y\right)=-1.386\cdot 2^{y}\)

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

\(f^\prime\left(y\right)=1.386\cdot 2^{y}\)

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

#15. \(s\left(z\right)=-z^4+3z^3-3z^2-2z+6\)

\(s^\prime\left(z\right)=-4z^3+9z^2-6z-2\)

\(s^\prime\left(z\right)=-z^4+3z^3-3z^2-2z+6\)

\(s^\prime\left(z\right)=4z^3-9z^2+6z+2\)

\(s^\prime\left(z\right)=z^4-3z^3+3z^2+2z-6\)

#16. \(g\left(y\right)=\frac{1}{y}\)

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

\(g^\prime\left(y\right)=\frac{1}{y^{2}}\)

\(g^\prime\left(y\right)=\frac{1}{y}\)

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

#17. \(h\left(x\right)=3\log x\)

\(h^\prime\left(x\right)=\frac{-1.303}{x}\)

\(h^\prime\left(x\right)=\frac{0.434}{x}\)

\(h^\prime\left(x\right)=\frac{1.303}{x}\)

\(h^\prime\left(x\right)=\log x\)

#18. \(f\left(z\right)=-6\cdot 2^{z}\)

\(f^\prime\left(z\right)=-2.773\cdot 2^{z}\)

\(f^\prime\left(z\right)=-2\cdot 2^{z}\)

\(f^\prime\left(z\right)=-4.159\cdot 2^{z}\)

\(f^\prime\left(z\right)=4\cdot 2^{z}\)

#19. \(s\left(z\right)=3\log z\)

\(s^\prime\left(z\right)=-3\log z\)

\(s^\prime\left(z\right)=\frac{-0.434}{z}\)

\(s^\prime\left(z\right)=\frac{1.303}{z}\)

\(s^\prime\left(z\right)=\frac{2.606}{z}\)

#20. \(f\left(y\right)=-\cos\left(y\right)\)

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

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

\(f^\prime\left(y\right)=4\sin\left(y\right)\)

\(f^\prime\left(y\right)=\sin\left(y\right)\)