Consider the following statements : Statement 1 : If y = log 10 x + log e x then \(\frac{dy}{dx}=\frac{\log_{10}e}{x}+\frac{1}{x}\) Statement 2 : \(\frac{d}{dx}(\log_{10}x)=\frac{\log x}{\log 10}\ \text{and}\ \frac{d}{dx}(\log_ex)=\frac{\log x}{\log e}\)

The correct answer is (A) : Statement 1 is true; statement 2 is false.

Statement 1 is true; statement 2 is false

Statement 1 is false; statement 2 is true

Both statements 1 and 2 are true

Both statements 1 and 2 are false

Statement 1 is true; statement 2 is false

Statement 1 is false; statement 2 is true

Both statements 1 and 2 are true

Both statements 1 and 2 are false

Statement 1:If y=log10x+logex then dy/dx=log10e/x+1/x Statement 2:d/dx(log10x)=logx/log10 and d/dx(loge x)=logx/loge

List-I	List-II
The derivative of \( \log_e x \) with respect to \( \frac{1}{x} \) at \( x = 5 \) is	(I) -5
If \( x^3 + x^2y + xy^2 - 21x = 0 \), then \( \frac{dy}{dx} \) at \( (1, 1) \) is	(II) -6
If \( f(x) = x^3 \log_e \frac{1}{x} \), then \( f'(1) + f''(1) \) is	(III) 5
If \( y = f(x^2) \) and \( f'(x) = e^{\sqrt{x}} \), then \( \frac{dy}{dx} \) at \( x = 0 \) is	(IV) 0