For the following equation, find (dy)/(dx). y=-x^(4)+9x^(2)-8x Answer: (dy)/(dx)=

Apply Power Rule: To find the derivative of the function y with respect to x, we will apply the power rule to each term separately. The power rule states that the derivative of x^n with respect to x is n*x^(n-1).Derivative of -x^4: First, we find the derivative of the term -x^(4). Using the power rule, we get: (dy)/(dx)(-x^(4)) = -4*x^(4-1) = -4x^3.Derivative of 9x^2: Next, we find the derivative of the term 9x^(2). Again, using the power rule, we get: (dy)/(dx)(9x^(2)) = 9*2*x^(2-1) = 18x.Derivative of -8x: Finally, we find the derivative of the term -8x. The power rule for the first power is simply the coefficient, so we get: (dy)/(dx)(-8x) = -8.Combine Derivatives: Now, we combine the derivatives of each term to find the derivative of the entire function y: (dy)/(dx) = -4x^3 + 18x - 8.

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Find derivatives of using multiple formulae

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Q. For the following equation, find

\frac{d y}{d x}

\newline

y=-x^{4}+9 x^{2}-8 x

\newline

Answer:

\frac{d y}{d x}=

Apply Power Rule: To find the derivative of the function $y$ with respect to $x$ , we will apply the power rule to each term separately. The power rule states that the derivative of $x^n$ with respect to $x$ is $n\cdot x^{(n-1)}$ .
Derivative of $-x^4$ : First, we find the derivative of the term $-x^{4}$ . Using the power rule, we get: $\newline$ $\frac{dy}{dx}(-x^{4}) = -4\cdot x^{4-1} = -4x^3$ .
Derivative of $9x^2$ : Next, we find the derivative of the term $9x^{2}$ . Again, using the power rule, we get: $\newline$ $\frac{dy}{dx}(9x^{2}) = 9\cdot2\cdot x^{2-1} = 18x$ .
Derivative of $-8x$ : Finally, we find the derivative of the term $-8x$ . The power rule for the first power is simply the coefficient, so we get: $\newline$ $\frac{dy}{dx}(-8x) = -8$ .
Combine Derivatives: Now, we combine the derivatives of each term to find the derivative of the entire function $y$ : $\frac{dy}{dx} = -4x^3 + 18x - 8.$