Resources

Resources

Bytelearn - cat image with glasses

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Evaluate: $f(x,y) = x\cos y + y\sin x$

View step-by-step help

View step-by-step help

Find derivatives using the quotient rule I

Full solution

Q. Evaluate:

f(x,y) = x\cos y + y\sin x

Identify function: Identify the function to differentiate. $f(x, y) = x\cos y + y\sin x$ .
Differentiate with x: Differentiate $f(x, y)$ with respect to $x$ . Using the product rule, derivative of $x\cos y$ with respect to $x$ is $\cos y$ (since derivative of $x$ is $1$ and derivative of $\cos y$ with respect to $x$ is $0$ ), and derivative of $x$ $0$ with respect to $x$ is $x$ $2$ (since derivative of $x$ $3$ with respect to $x$ is $x$ $5$ ). So, $x$ $6$ .
Differentiate with $y$ : Differentiate $f(x, y)$ with respect to $y$ . Using the product rule, derivative of $x\cos(y)$ with respect to $y$ is $-x\sin(y)$ (since derivative of $\cos(y)$ with respect to $y$ is $-\sin(y)$ and $x$ is treated as a constant), and derivative of $f(x, y)$ $0$ with respect to $y$ is $f(x, y)$ $2$ (since derivative of $y$ is $f(x, y)$ $4$ and $f(x, y)$ $2$ is treated as a constant). So, $f(x, y)$ $6$ .

More problems from Find derivatives using the quotient rule I

Question

Find the derivative of

f(x)

\newline

f(x) = \cos(x)

\newline

f'(x) =

Posted 5 months ago

Question

Find the derivative of

f(x)

\newline

f(x) = \tan(x)

\newline

f'(x) =

Posted 6 months ago

Question

Find the derivative of

f(x)

\newline

f(x) = e^x

\newline

f'\left(x\right) =

Posted 6 months ago

Question

Find the derivative of

f(x)

\newline

f(x) = \ln(x)

\newline

f'(x) =

Posted 6 months ago

Question

Find the derivative of

f(x)

\newline

f(x) = \tan^{-1}{x}

\newline

f'(x) =

Posted 6 months ago

Question

Find the derivative of

f(x)

\newline

f(x) = x e^x

\newline

f'\left(x\right) =

Posted 6 months ago

Question

Find the derivative of

f(x)

\newline

f(x) = \frac{e^x}{x}

\newline

f'(x) =

Posted 6 months ago

Question

Find the derivative of

f(x)

\newline

f(x) = e^{(x + 1)}

\newline

f'\left(x\right) =

Posted 5 months ago

Question

Find the derivative of

f(x)

\newline

f(x) = \sqrt{x+3}

\newline

f'(x) =

Posted 6 months ago

Question

Find the derivative of

g(x)

\newline

g(x) = \ln(2x)

\newline

g^{\prime}(x) =

Posted 7 months ago

Related topics

Algebra - Order of Operations Algebra - Distributive Property `X` and `Y` Axes Geometry - Scalene Triangle Common Multiple Geometry - Quadrant