Question

3. Consider the curve with equation: \[ 2 y+\sin (y)+5=x^{4}+4 x^{3}+2 \pi \] Use implicit differentiation to find an expression for \( y^{\prime} \) in terms of \( x \) and \( y \). When \( x=1 \) calculate the value of \( y^{\prime} \).

          3. Consider the curve with equation:
\[
2 y+\sin (y)+5=x^{4}+4 x^{3}+2 \pi
\]

Use implicit differentiation to find an expression for \( y^{\prime} \) in terms of \( x \) and \( y \). When \( x=1 \) calculate the value of \( y^{\prime} \).

3. Consider the curve with equation:

2 y+sin (y)+5=x^4+4 x^3+2 π

Use implicit differentiation to find an expression for y^' in terms of x and y. When x=1 calculate the value of y^'.

Added by Brandon G.

Calculus

James Stewart 4th Edition

Chapter 3

Instant Answer

Solved by Expert Shaiju T

Step 1

The given equation is: \[ 2y + \sin(y) + 5 = x^4 + 4x^3 + 2\pi \] Differentiate the left side: - The derivative of \( 2y \) with respect to \( x \) is \( 2y' \). - The derivative of \( \sin(y) \) with respect to \( x \) is \( \cos(y) \cdot y' \) (using the chain Show more…

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3. Consider the curve with equation: \[ 2 y+\sin (y)+5=x^{4}+4 x^{3}+2 \pi \] Use implicit differentiation to find an expression for \( y^{\prime} \) in terms of \( x \) and \( y \). When \( x=1 \) calculate the value of \( y^{\prime} \).