Find the derivative of ( 2

oglasnak9h01

oglasnak9h01

Answered question

2022-04-04

Find the derivative of ( 2 x )  tan ( π x ).

Answer & Explanation

rotgelb7kjxw

rotgelb7kjxw

Beginner2022-04-05Added 16 answers

Since 2 is constant with respect to x, the derivative of (2x)tan(πx) with respect to x is 2ddx[(x)tan(πx)].

2ddx[(x)tan(πx)]

Differentiate using the Product Rule which states that ddx[f(x)g(x)] is f(x)ddx[g(x)]+g(x)ddx[f(x)] where f(x)=x and gg(x)=tan(πx).

2(xddx[tan(πx)]+tan(πx)ddx[x])

Differentiate using the chain rule, which states that ddx[f(g(x))] is f(g(x))g(x) where f(x)=tan(x) and g(x)=πx.

2(x(sec2(πx)ddx[πx])+tan(πx)ddx[x])

Differentiate.

2(x(sec2(πx)π)+tan(πx))

Simplify.

2πxsec2(πx)+2tan(πx)

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