If F(x) = f(x)g(x)h(x) and F’(x) = 10F(x) and f’(x) = 10f(x) , g’(x) = 10g(x) and h’(x) = 10kh(x), then find value of k.
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Answer:
F
′
(x)=f
′
(x)g(x)h(x)+f(x)g
′
(x)h(x)+f(x)g(x)h
′
(x)
so ,21F(x
0
)=F
′
(x
0
)=f
′
(x
0
)g(x
0
)h(x
0
)+f(x
0
)g
′
(x
0
)h(x
0
)+f(x
0
)g(x
0
)h
′
(x
0
)
=4f(x
0
)g(x
0
)h(x
0
)−7f(x
0
)g(x
0
)h(x
0
)+kf(x
0
)g(x
0
)h(x
0
)
=(−3+k)f(x
0
)g(x
0
)h(x
0
)
=(−3+k)F(x
0
)
Hence 21=−3+k⇒k=24
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