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1636370327
Calculus Derivative Formulas (Easy)
Name __________
Find the derivative of the given function.
#1.
\(g\left(x\right)=2\ln\left(x\right)\)
\(g^\prime\left(x\right)=6\ln\left(x\right)\)
\(g^\prime\left(x\right)=\frac{-4}{x}\)
\(g^\prime\left(x\right)=\frac{2}{x}\)
\(g^\prime\left(x\right)=\frac{6}{x}\)
#2.
\(g\left(x\right)=-6\cdot 4^{x}\)
\(g^\prime\left(x\right)=-1\cdot 4^{x}\)
\(g^\prime\left(x\right)=-3\cdot 4^{x}\)
\(g^\prime\left(x\right)=-6.931\cdot 4^{x}\)
\(g^\prime\left(x\right)=-8.318\cdot 4^{x}\)
#3.
\(g\left(y\right)=2e^{y}\)
\(g^\prime\left(y\right)=-2e^{y}\)
\(g^\prime\left(y\right)=2e^{y}\)
\(g^\prime\left(y\right)=5e^{y}\)
\(g^\prime\left(y\right)=e^{y}\)
#4.
\(f\left(t\right)=3^{t}\)
\(f^\prime\left(t\right)=-1.099\cdot 3^{t}\)
\(f^\prime\left(t\right)=-1\cdot 3^{t}\)
\(f^\prime\left(t\right)=1.099\cdot 3^{t}\)
\(f^\prime\left(t\right)=4.394\cdot 3^{t}\)
#5.
\(h\left(y\right)=-1\sqrt{y}\)
\(h^\prime\left(y\right)=5\sqrt{y}\)
\(h^\prime\left(y\right)=\frac{-\frac{1}{2}}{\sqrt{y}}\)
\(h^\prime\left(y\right)=\frac{1}{\sqrt{y}}\)
\(h^\prime\left(y\right)=\frac{\frac{5}{2}}{\sqrt{y}}\)
#6.
\(s\left(y\right)=-3e^{y}\)
\(s^\prime\left(y\right)=-2e^{y}\)
\(s^\prime\left(y\right)=-3e^{y}\)
\(s^\prime\left(y\right)=2e^{y}\)
\(s^\prime\left(y\right)=3e^{y}\)
#7.
\(s\left(y\right)=2\cdot 2^{y}\)
\(s^\prime\left(y\right)=0.693\cdot 2^{y}\)
\(s^\prime\left(y\right)=1.386\cdot 2^{y}\)
\(s^\prime\left(y\right)=2.773\cdot 2^{y}\)
\(s^\prime\left(y\right)=2^{y}\)
#8.
\(g\left(y\right)=-1\cdot 6^{y}\)
\(g^\prime\left(y\right)=-1.792\cdot 6^{y}\)
\(g^\prime\left(y\right)=-5\cdot 6^{y}\)
\(g^\prime\left(y\right)=5\cdot 6^{y}\)
\(g^\prime\left(y\right)=8.959\cdot 6^{y}\)
#9.
\(h\left(z\right)=4\cot\left(z\right)\)
\(h^\prime\left(z\right)=-4\cot\left(z\right)\)
\(h^\prime\left(z\right)=-4csc^{2}\left(z\right)\)
\(h^\prime\left(z\right)=5csc^{2}\left(z\right)\)
\(h^\prime\left(z\right)=6csc^{2}\left(z\right)\)
#10.
\(f\left(t\right)=-5e^{t}\)
\(f^\prime\left(t\right)=-2e^{t}\)
\(f^\prime\left(t\right)=-5e^{t}\)
\(f^\prime\left(t\right)=2e^{t}\)
\(f^\prime\left(t\right)=5e^{t}\)
#11.
\(s\left(y\right)=\frac{1}{y^{5}}\)
\(s^\prime\left(y\right)=\frac{-15}{y^{6}}\)
\(s^\prime\left(y\right)=\frac{-5}{y^{6}}\)
\(s^\prime\left(y\right)=\frac{15}{y^{6}}\)
\(s^\prime\left(y\right)=\frac{4}{y^{5}}\)
#12.
\(f\left(x\right)=-\log x\)
\(f^\prime\left(x\right)=2\log x\)
\(f^\prime\left(x\right)=\frac{-0.434}{x}\)
\(f^\prime\left(x\right)=\frac{-1.303}{x}\)
\(f^\prime\left(x\right)=\frac{1.303}{x}\)
#13.
\(s\left(x\right)=-5\cdot 4^{x}\)
\(s^\prime\left(x\right)=-3\cdot 4^{x}\)
\(s^\prime\left(x\right)=-4.159\cdot 4^{x}\)
\(s^\prime\left(x\right)=-6.931\cdot 4^{x}\)
\(s^\prime\left(x\right)=8.318\cdot 4^{x}\)
#14.
\(h\left(x\right)=x^3+3x^2+3x+2\)
\(h^\prime\left(x\right)=-3x^2-6x-3\)
\(h^\prime\left(x\right)=-x^3-3x^2-3x-2\)
\(h^\prime\left(x\right)=3x^2+6x+3\)
\(h^\prime\left(x\right)=x^3+3x^2+3x+2\)
#15.
\(f\left(x\right)=-3e^{x}\)
\(f^\prime\left(x\right)=-2e^{x}\)
\(f^\prime\left(x\right)=-3e^{x}\)
\(f^\prime\left(x\right)=2e^{x}\)
\(f^\prime\left(x\right)=3e^{x}\)
#16.
\(g\left(t\right)=3e^{t}\)
\(g^\prime\left(t\right)=-2e^{t}\)
\(g^\prime\left(t\right)=2e^{t}\)
\(g^\prime\left(t\right)=3e^{t}\)
\(g^\prime\left(t\right)=e^{t}\)
#17.
\(h\left(z\right)=3\cdot 2^{z}\)
\(h^\prime\left(z\right)=-2.079\cdot 2^{z}\)
\(h^\prime\left(z\right)=-4\cdot 2^{z}\)
\(h^\prime\left(z\right)=2.079\cdot 2^{z}\)
\(h^\prime\left(z\right)=2.773\cdot 2^{z}\)
#18.
\(s\left(y\right)=5\log y\)
\(s^\prime\left(y\right)=4\log y\)
\(s^\prime\left(y\right)=\frac{-0.434}{y}\)
\(s^\prime\left(y\right)=\frac{1.737}{y}\)
\(s^\prime\left(y\right)=\frac{2.171}{y}\)
#19.
\(h\left(z\right)=-2\sec\left(z\right)\)
\(h^\prime\left(z\right)=-2\sec\left(z\right)\tan\left(z\right)\)
\(h^\prime\left(z\right)=-\sec\left(z\right)\)
\(h^\prime\left(z\right)=2\sec\left(z\right)\)
\(h^\prime\left(z\right)=2\sec\left(z\right)\tan\left(z\right)\)
#20.
\(g\left(y\right)=2\sec\left(y\right)\)
\(g^\prime\left(y\right)=-6\sec\left(y\right)\tan\left(y\right)\)
\(g^\prime\left(y\right)=2\sec\left(y\right)\tan\left(y\right)\)
\(g^\prime\left(y\right)=6\sec\left(y\right)\)
\(g^\prime\left(y\right)=\sec\left(y\right)\)
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