MHT CET · Maths · Differentiation
If \(y=2^{a x}\) and \(\left(\frac{d y}{d x}\right)_{x=1}=\log 256\), then \(a=\)
- A 4
- B 2
- C 8
- D 3
Answer & Solution
Correct Answer
(B) 2
Step-by-step Solution
Detailed explanation
\(y=2^{2 x} \Rightarrow \frac{d y}{d x}=2^{2 x}(\log 2)(a)\)
\(\therefore\left(\frac{d y}{d x}\right)_{x=1}=\left(2^{a}\right)(a)(\log 2)\)
As per condition given
\(\left(2^{a}\right)(a)(\log 2)=\log 256=\log (2)^{8}=8 \log 2\)
\(\therefore\left(2^{a}\right)(a)=8 \Rightarrow a=2\)
\(\therefore\left(\frac{d y}{d x}\right)_{x=1}=\left(2^{a}\right)(a)(\log 2)\)
As per condition given
\(\left(2^{a}\right)(a)(\log 2)=\log 256=\log (2)^{8}=8 \log 2\)
\(\therefore\left(2^{a}\right)(a)=8 \Rightarrow a=2\)
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