Pertanyaan

Jika f x = sin x + cos x sin x – cos x , maka f′(0°) = ….

Jika $begin mathsize 14px style straight f open parentheses straight x close parentheses equals fraction numerator sinx straight space plus space cosx over denominator sinx straight space – straight space cosx end fraction end style$ , maka f′(0°) = ….

– 4
– 2
– 1
0
1

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H. Eka

Master Teacher

Mahasiswa/Alumni Universitas Pendidikan Indonesia

Jawaban terverifikasi

Pembahasan

JIka y = u v maka y ' = u ' v - u v ' v 2 u = sin x + cos x u′ = cos x− sin x v = sin x −cos x v′ = cos x +sin x maka :

JIka maka $begin mathsize 14px style straight y to the power of straight apostrophe equals fraction numerator straight u to the power of straight apostrophe straight v straight space minus straight u straight space straight v to the power of straight apostrophe over denominator straight v squared end fraction end style$

u = sin x + cos x
u′ = cos x − sin x

v = sin x − cos x
v′ = cos x + sin x

maka :

$begin mathsize 14px style straight f to the power of straight apostrophe open parentheses straight x close parentheses equals fraction numerator open parentheses cos space straight x minus sin space straight x close parentheses open parentheses sin space straight x minus cos space straight x close parentheses minus open parentheses sin space straight x plus cos space straight x close parentheses open parentheses cos space straight x plus sin space straight x close parentheses over denominator open parentheses sin space straight x minus cos space straight x close parentheses squared end fraction straight f to the power of straight apostrophe open parentheses 0 degree close parentheses equals fraction numerator open parentheses 1 minus 0 close parentheses open parentheses 0 minus 1 close parentheses minus left parenthesis 0 plus 1 right parenthesis left parenthesis 1 plus 0 right parenthesis over denominator open parentheses 0 minus 1 close parentheses squared end fraction straight f to the power of straight apostrophe open parentheses 0 degree close parentheses equals negative 2 over 1 equals negative 2 end style$