Find the derivative of e <mrow class="MJX-TeXAtom-ORD"> x </mrow> </msup>

junoonib89p4

junoonib89p4

Answered question

2022-05-06

Find the derivative of e x  cos ( π x ).

Answer & Explanation

nelppeazy9v3ie

nelppeazy9v3ie

Beginner2022-05-07Added 22 answers

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)=ex and g(x)=cos(πx).

exddx[cos(πx)]+cos(πx)ddx[ex]

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

ex(-sin(πx)ddx[πx])+cos(πx)ddx[ex]

Differentiate.

ex(-sin(πx)π)+cos(πx)ddx[ex]

Differentiate using the Exponential Rule which states that ddx[ax] is axln(a) where a=e.

ex(-sin(πx)π)+cos(πx)ex

Reorder terms.

πexsin(πx)+excos(πx)

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