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3 years ago

What is the derivative of y=3tan(x)y=3 tan (x) ?

Mathematics

2 answers:

maw [93]3 years ago

6 0

$y=3tanx\\\\tanx=\frac{sinx}{cosx}\Rightarrow y=\frac{3sinx}{cosx}\\\\\\y'=\frac{(3sinx)'cosx-3sinx(cosx)'}{(cosx)^2}=\frac{3cosxcosx-3sinx(-sinx)}{cos^2x}=\frac{3cos^2x+3sin^2x}{cos^2x}\\\\=\frac{3(cos^2x+sin^2x)}{cos^2x}=\frac{3(1)}{cos^2x}=\frac{3}{cos^2x}\\\\-------------------\\\\sin^2x+cos^2x=1$

viva [34]3 years ago

6 0

Answer is in the attachment below. Use the "product rule".

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