Let ð‘“ be a function which is everywhere differentiable and for which ð‘“(2) = −3 and 𑓠′ (ð‘¥) = √𑥠2 + 5. Given that ð‘” is defined such that ð‘”(ð‘¥) = ð‘¥ 2ð‘“ ( 𑥠𑥠− 1 ), show that 𑔠′ (2) = −24.
Given that "f'(x)=\\sqrt{x^2+5}"
"g(x)=x^2(f(x)-1)"
Differentiating "g(x)" w.r.t ."x," we get:
"g'(x)=2x(f(x)-1)+x^2(f'(x))"
Put "x=2"
"g'(2)=4(f(2)-1)+2^2(f'(2))"
"=4((-3)-1)+4f'(2)\\\\\n=-16+4(3)\\\\\n=-4"
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