The differential of ${\mathrm{e}}^{{\mathrm{x}}^3}$ with respect to $\log \mathrm{x}\mathrm{ }$ is -

Important Questions on Continuity and Differentiability

EASY

CUET (UG)

IMPORTANT

Achieve CUET (UG) Mathematics Practice Book>Chapter 5 - Continuity and Differentiability>Exercise>Q 54

If $\mathrm{x}={\mathrm{e}}^{\mathrm{y}\mathrm{ }+\mathrm{ }{\mathrm{e}}^{\mathrm{y}\mathrm{ }+\mathrm{ }{\mathrm{e}}^{\mathrm{y}\mathrm{ }+\mathrm{ }{\mathrm{e}}^{\mathrm{y}\mathrm{ }+....\mathrm{\infty }}}}}$ , then $\frac{\mathrm{d}\mathrm{y}}{\mathrm{d}\mathrm{x}}$ is

EASY

CUET (UG)

IMPORTANT

Achieve CUET (UG) Mathematics Practice Book>Chapter 5 - Continuity and Differentiability>Exercise>Q 55

$\frac{d}{dx} \left[x^x+x^a+a^x+a^a\right]=\dots ;a$ is constant

EASY

CUET (UG)

IMPORTANT

Achieve CUET (UG) Mathematics Practice Book>Chapter 5 - Continuity and Differentiability>Exercise>Q 56

$\frac{d}{dx}\left[x^x+x^a+a^x+a^a\right]$ is equal to (where $a$ is constant)

EASY

CUET (UG)

IMPORTANT

Achieve CUET (UG) Mathematics Practice Book>Chapter 5 - Continuity and Differentiability>Exercise>Q 57

Differentiate $x^{\sin x}, x>0$ with respect to $x$.

EASY

CUET (UG)

IMPORTANT

Achieve CUET (UG) Mathematics Practice Book>Chapter 5 - Continuity and Differentiability>Exercise>Q 58

If $y=e^{x+e^{x+...\infty }}$ then $\frac{dy}{dx}=?$

MEDIUM

CUET (UG)

IMPORTANT

Achieve CUET (UG) Mathematics Practice Book>Chapter 5 - Continuity and Differentiability>Exercise>Q 59

If ${\mathrm{x}}^{\mathrm{y}}={\mathrm{e}}^{\mathrm{x}-\mathrm{ }\mathrm{y}}$ , then $\frac{dy}{dx}$ is equal to

MEDIUM

CUET (UG)

IMPORTANT

Achieve CUET (UG) Mathematics Practice Book>Chapter 5 - Continuity and Differentiability>Exercise>Q 60

If $x^y=e^{x\mathit{-}y}$, then $\frac{dy}{dx}$ is equal to:

MEDIUM

CUET (UG)

IMPORTANT

Achieve CUET (UG) Mathematics Practice Book>Chapter 5 - Continuity and Differentiability>Exercise>Q 61

Let $y=x^{x^{x\dots }}$, then $\frac{dy}{dx }$is equal to