How do you find the derivative of #S(r)=9r^2+3tanr#?

Answer 1

#S'(r)=18r+3sec^2r#

differentiate the first term using the #color(blue)"power rule"# and use the #color(blue)"standard derivative for tan"#

#color(orange)"Reminder " color(red)(bar(ul(|color(white)(2/2)color(black)(d/dx(ax^n)=nax^(n-1))color(white)(2/2)|)))" power rule"#

#color(red)(bar(ul(|color(white)(2/2)color(black)(d/dx(tanx)=sec^2x)color(white)(2/2)|)))#

#S(r)=9r^2+3tanr#

#rArrS'(r)=18r+3sec^2r#

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Answer 2

Emilia Aguilar

To find the derivative of ( S(r) = 9r^2 + 3 \tan(r) ), you apply the power rule and the derivative of tangent function.

The derivative of ( 9r^2 ) with respect to ( r ) using the power rule is ( 18r ).

The derivative of ( 3 \tan(r) ) with respect to ( r ) can be found using the derivative of tangent function which is ( \sec^2(r) ).

Therefore, the derivative of ( S(r) ) is ( S'(r) = 18r + 3 \sec^2(r) ).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.