Question 47

Mathematics Differentiation Hard

The derivatives of (x<sup>3</sup> + e<sup>x</sup> + 3<sup>x</sup> + cot x) with respect to x is

(A) 3x<sup>2</sup> + e<sup>x</sup> + 3<sup>x</sup> (log 3) - cos ec<sup>2</sup> x
(B) 3x<sup>2</sup> + e<sup>x</sup> + 3<sup>x</sup> (log 3) + cos ec<sup>2</sup> x
(C) 3x<sup>2</sup> + e<sup>x</sup> + 3<sup>x</sup> (log 3) - sec<sup>2</sup> x
(D) 3x<sup>2</sup> + e<sup>x</sup> + 3<sup>x</sup> (log 3) + sec<sup>2</sup> x
View Dynamic Solution & Explanation
Correct Solution: Option A

Step-by-step Solution:

Concept: \[ \frac{d}{dx} (a^x) = a^x \ln a \] \[ \frac{d}{dx} (\cot x) = -\csc^2 x \] --- Calculation: \[ \frac{d}{dx} \left( x^3 + e^x + 3^x + \cot x \right) \] Applying differentiation: \[ = 3x^2 + e^x + 3^x \ln 3 - \csc^2 x \] --- Conclusion: Hence, option (1) is correct.