Resourcesdown chevron
Testimonials
Plans
Sign in
Sign up
Resourcesright arrow
Testimonials
Plans
Bytelearn - cat image with glassesAI tutor

Welcome to Bytelearn!

Let’s check out your problem:

dydx=y−1x−3\frac{dy}{dx}=y^{-1}x^{-3}

View step-by-step helpView step-by-step help
Homeright chevron icon
Math Problemsright chevron icon
Algebra 2right chevron icon
Composition of linear and quadratic functions: find a valueright chevron icon

Full solution

Q. dydx=y−1x−3\frac{dy}{dx}=y^{-1}x^{-3}
  1. Identify Function: Identify the function to differentiate.\newlineWe need to find the derivative of y=y−1x−3y = y^{-1}x^{-3} with respect to xx.
  2. Apply Product Rule: Apply the product rule for differentiation.\newlineThe product rule states that (uv)′=u′v+uv′(uv)' = u'v + uv', where uu and vv are functions of xx.\newlineHere, u=y−1u = y^{-1} and v=x−3v = x^{-3}.
  3. Differentiate Functions: Differentiate each function.\newlineFor u=y−1u = y^{-1}, the derivative u′=−1×y−2×dydxu' = -1 \times y^{-2} \times \frac{dy}{dx} (using chain rule).\newlineFor v=x−3v = x^{-3}, the derivative v′=−3x−4v' = -3x^{-4} (using power rule).
  4. Substitute into Formula: Substitute back into the product rule formula.\newline(dydx)=(−1×y−2×dydx)×x−3+y−1×(−3x−4)(\frac{dy}{dx}) = (-1 \times y^{-2} \times \frac{dy}{dx}) \times x^{-3} + y^{-1} \times (-3x^{-4})

More problems from Composition of linear and quadratic functions: find a value

Question
Find the inverse of the function. y=x+3 y = x + 3 Write your answer in the form ax+b ax + b . Simplify any fractions. y= y = _____
Get tutor helpright-arrow

Posted 3 months ago

Question
Find (r∘s)(x)(r \circ s)(x).\newliner(x) = 33x\newlines(x) = 22x + 55\newlineWrite your answer as a polynomial in simplest form.\newline(r∘s)(x)=(r \circ s)(x) = ____
Get tutor helpright-arrow

Posted 2 months ago

Question
What is (f+g)(x)(f + g)(x)?\newlinef(x)=−3xf(x) = -3x\newlineg(x)=3x+1g(x) = 3x + 1\newline\newlineWrite your answer as a polynomial or a rational function in simplest form.\newline‾\underline{\hspace{3cm}}\newline
Get tutor helpright-arrow

Posted 2 months ago

Question
What is (f∗g)(x)(f * g)(x)?\newlinef(x)=−x+4f(x) = -x + 4\newlineg(x)=4xg(x) = 4x\newline\newlineWrite your answer as a polynomial or a rational function in simplest form.\newline‾\underline{\hspace{3em}}\newline
Get tutor helpright-arrow

Posted 2 months ago

Question
What is the domain of (fg)(x)\left(\frac{f}{g}\right)(x)?\newlinef(x)=2xf(x) = 2x\newlineg(x)=−5x+3g(x) = -5x + 3\newlineChoices:\newline[A]All real numbers[\text{A]All real numbers}\newline[B]All real numbers except 35[\text{B]All real numbers except } \frac{3}{5}\newline[C]All real numbers except −35[\text{C]All real numbers except } -\frac{3}{5}\newline[D]All real numbers except 53[\text{D]All real numbers except } \frac{5}{3}
Get tutor helpright-arrow

Posted 3 months ago

Question
Find the inverse of the function.\newliney = −3x-3x \newlineWrite your answer in the form ax+bax + b. Simplify any fractions.\newliney = ______
Get tutor helpright-arrow

Posted 2 months ago

Question
Find (f∘g)(0)(f \circ g)(0).\newlinef(x)=6xf(x) = 6x\newlineg(x)=x2+4xg(x) = x^2 + 4x\newline(f∘g)(0)=(f \circ g)(0) = ____
Get tutor helpright-arrow

Posted 2 months ago

Question
Find (f∘g)(x)(f \circ g)(x).\newlinef(x)=x2+5f(x) = x^2 + 5\newlineg(x)=4xg(x) = 4x\newlineWrite your answer as a polynomial in simplest form.\newline(f∘g)(x)=(f \circ g)(x) = ______
Get tutor helpright-arrow

Posted 2 months ago

Question
Is f(x) f(x) the inverse function of g(x) g(x) ?\newlinef(x)=x f(x) = x \newlineg(x)=−4x g(x) = -4x \newlineChoices:\newline[yes] \text{[yes]} \newline[no] \text{[no]}
Get tutor helpright-arrow

Posted 2 months ago

Question
What is (f∗g)(x)(f * g)(x)? f(x)=3x2+9xf(x) = 3x^2 + 9x g(x)=3xg(x) = 3x Write your answer as a polynomial or a rational function in simplest form. ______
Get tutor helpright-arrow

Posted 3 months ago

View all (200)