Objective Questions

Find dy/dx if y = e^sin2x / cos2x.

Find dy/dx if y = log_e(cos x).

If y = ∫ f(x)dx + C, then ∫ f(x)dx is called the -----.

Evaluate ∫ Cos(ln x) / x dx.

Evaluate ∫ Cos³ x dx.

Find the derivative $\frac{dy}{dx}$ if $y = x^{\tan x}$.

If $y = e^{2x} \log(x+6)$, find $\frac{dy}{dx}$. (Assume $\log$ denotes the nat…

Evaluate the integral $\int \frac{\cos(\ln x)}{x} dx$.

Simplify the integral $\int 3x^2 e^{x^3} dx$.

Find $\frac{dy}{dx}$ if $3x^2y + xy^2 = 5$ using implicit differentiation.

Differentiate the implicit function $x^2 \sin y - e^{2y} \cos x = 3x^2 + 2x - 5…

Obtain $\frac{d}{dx} \left[ \ln\left(\frac{x^2}{x^2+1}\right) \right]$.

Simplify the integral $\int \frac{4x-5}{x^2-x-2} dx$.

Evaluate $\int \cos^3 x dx$.

If $y = \int f(x)dx + C$, then $\int f(x)dx$ is called the -----.

Evaluate $\int \frac{e^{2x} + e^{-2x}}{e^{2x} - e^{-2x}} dx$.

Evaluate $\int \frac{dx}{x^2 + 4x + 7}$.

Find $\frac{dy}{dx}$, if $y = \log_e \cos x$.

Which of the following equations related to integrals is not correct?

If $y = \frac{e^{\sin 2x}}{\cos 2x}$, find $\frac{dy}{dx}$.

Find dy/dx if y = x^{tan x}.

If y = e^2x log(x+6), find dy/dx. (Assume 'log' denotes…

Evaluate ∫ Cos(lnx)/x dx.

Simplify ∫ 3x²e^x3 dx.

Find dy/dx if 3x²y + xy² = 5.

Differentiate the implicit function x² siny - e^2y cosx…

Obtain d/dx [ln(x² / (x²+1))].

Simplify ∫ (4x-5) / (x²-x-2) dx.

If y = e^sin2x / cos2x, find dy/dx. (Assume e^si…

Evaluate ∫ Cos³(x) dx.

Evaluate ∫ (e^2x + e^-2x) / (e^2x - e^…

Evaluate ∫ dx / (x² + 4x + 7).

Find dy/dx, if y = log_e(cos x).

Which of the following equations is not correct?

Obtain \( \frac{d}{dx}\left[\ln\left(\frac{x^2}{x^2+1}\right)\right] \)

Differentiate \( y = \log(x^3 - x) + 7^{3x} \)

Differentiate the implicit functions \( x^2 \sin(y) - e^{2y} \cos(x) = 3x^2 + 2…

Evaluate \( \int \frac{dx}{x^2+4x+7} \)

Simplify \( \int \frac{4x-5}{x^2-x-2} dx \)

Find \( \frac{dy}{dx} \) if \( 3x^2 y + xy^2 = 5 \)

If \( y = e^{2x} \log(x+6) \), find \( \frac{dy}{dx} \)

Find \( \frac{dy}{dx} \) if \( y = x^{\tan x} \)

Evaluate \( \int \frac{e^{2x} + e^{-2x}}{e^{2x} - e^{-2x}} dx \)

Find \( dy/dx \) for \( y = \ln(x \sin x) \).

If \( y = x^x \), find \( dy/dx \).

Find \( dy/dx \) for \( y = e^{-x} \sin 3x \).

What is the derivative of \( y = 1/x^2 \)?

If \( y = \ln 10 \), find \( dy/dx \).

The rate of change of area \( A \) with respect to \( x \) if \( A = \pi x^2 - …

Evaluate \( \int \cos^3 x \,dx \)

Find \( \frac{dy}{dx} \) if \( y = \log_e(\cos x) \)

If \( y = \frac{e^{\sin(2x)}}{\cos(2x)} \), find \( \frac{dy}{dx} \)

Find the coordinates of the local maximum for \( y = x^2 - 6\sqrt{x^4} + 2 \).

What is the derivative of \( y = \sec x \)?

Differentiate \( y = \sin^2 x \).

Differentiate the implicit functions $x^2 \sin y - e^{2y} \cos x = 3x^2 + 2x - …

Simplify $\int 3x^2 e^{x^3} dx$.

Simplify $\int \frac{4x - 5}{x^2 - x - 2} dx$.

If $y = e^{2x} \log(x+6)$, find $\frac{dy}{dx}$. (Assume $\log$ denotes the nat…

Find $\frac{dy}{dx}$ if $y = x^{\tan x}$.

Differentiate \( y = (x-a)(x-b) \).

Find $\frac{dy}{dx}$, if $y = \log_e (\cos x)$.

Which of the following equations related to integrals is NOT correct?

Find $\frac{dy}{dx}$ if $3x^2 y + xy^2 = 5$.

Obtain $\frac{d}{dx} \left(\ln\left(\frac{x^2}{x^2+1}\right)\right)$.

Differentiate $y = \log(x^3 - x) + 7^{3x}$. (Assume $\log$ denotes the natural …

Obtain $\frac{d}{dx}\left[\ln\left(\frac{x^2}{x^2+1}\right)\right]$

Differentiate $y = \log(x^3 - x) + 7^{3x}$.
(Note: Assuming a typo in the…

Simplify $\int 3x^2 e^{x^3} dx$

Evaluate $\int \frac{dx}{x^2+4x+7}$

Simplify $\int \frac{4x-5}{x^2-x-2} dx$

Find $\frac{dy}{dx}$ if $3x^2 y + xy^2 = 5$

If $y = e^{2x} \log (x+6)$, find $\frac{dy}{dx}$.
(Note: Assuming $\log$ …

Find $\frac{dy}{dx}$ if $y = x^{\tan x}$

Evaluate $\int \frac{e^{2x} + e^{-2x}}{e^{2x} - e^{-2x}} dx$

Evaluate $\int \cos^3 x dx$

If $y = \int f(x)dx + C$, then $f(x)dx$ is called the -----.

Obtain the derivative of the implicit function x² siny…

Differentiate y = log(x³ - x) + 7^(3/x

Obtain d/dx { ln (x² / (x²

Simplify ∫ (4x - 5) / (x² - x -…

Find dy/dx if y = x^{tan x}

Find dy/dx if 3x²y + xy² = 5

Find dy/dx if y = log_e(cos x)

Evaluate ∫ cos³ x dx

If y = e^2x log (x+6), find dy/dx

Evaluate ∫ (e^2x + e^-2x

Simplify ∫ 3x²e^x3 …

If $y = \int f(x)dx + C$, then $f(x)$ is called the _____.

Differentiate the implicit function x² sin y - e^2y cos…

Find dy/dx if y = x^{tan x}.

If y = e^sin(2x) / cos(2x), find dy/dx.

Obtain d/dx [ln(x²/(x²+1))].

Simplify ∫ (4x-5)/(x²-x-2) dx.

Simplify ∫ 3x²e^x3 dx.

Evaluate ∫ Cos³ x dx.

Evaluate ∫ dx/(x²+4x+7).

Simplify ∫ e^x sin x dx.

If y = ∫ f(x)dx + C, then f(x)dx is called the _______.

Differentiate y = log(x³ - x) + 7^3x