Find f’ in terms of g’. f(x)=x2g(x)

Name: Find f’ in terms of g’. f(x)=x2g(x)
Uploaded: 2022-02-23T17:22:57+00:00
Description: Find f’ in terms of g’. f(x)=x2g(x)

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Find f’ in terms of g’.  f(x)=x2g(x)

Vincent Diaz · Accepted Answer

f(x)=x2g(x)Differentiate with respect to xf′(x)=d[x2g(x)]dxThe Product Rule for differentiation[f(x)⋅g(x)]′=f′(x)⋅g(x)+f(x)⋅g′(x)f′(x)=d(x2)dx⋅g(x)+x2⋅d[g(x)]dxThe Power RuleIf n is a non-zero real number, then d(xn)dx=nxn−1f′(x)=2x2−1⋅g(x)+x2⋅g′(x)f′(x)=2x⋅g(x)+x2⋅g′(x)Result:f′(x)=2x⋅g(x)+x2⋅g′(x)

Eliza Beth13 · Accepted Answer

To find the derivative of f in terms of g′, we can use the product rule of differentiation. The product rule states that if we have two functions u(x) and v(x), then the derivative of their product uv is given by:(uv)′=u′v+uv′In this case, u(x)=x2 and v(x)=g(x). We can differentiate each of these functions separately:u′(x)=2xandv′(x)=g′(x)Applying the product rule, we have:f′(x)=(x2)′g(x)+x2g′(x)Simplifying this expression, we get:f′(x)=2xg(x)+x2g′(x)Therefore, the derivative of f in terms of g′ is 2xg(x)+x2g′(x).

madeleinejames20 · Accepted Answer

Step 1: Given:f′(x)=u′(x)·v(x)+u(x)·v′(x)In our case, f(x)=x2·g(x), where u(x)=x2 and v(x)=g(x). To find f′(x), we need to find the derivatives of u(x) and v(x), denoted as u′(x) and v′(x) respectively.Let&#039;s start by finding u′(x):u(x)=x2Using the power rule for differentiation, we have:u′(x)=2xStep 2: Now, let&#039;s find v′(x):v(x)=g(x)We are given that g′(x) is the derivative of g(x), so we can simply write:v′(x)=g′(x)Finally, we can substitute these values into the product rule formula:f′(x)=u′(x)·v(x)+u(x)·v′(x)f′(x)=(2x)·g(x)+(x2)·g′(x)Hence, the derivative of f(x)=x2·g(x) with respect to x is given by f′(x)=(2x)·g(x)+(x2)·g′(x).

Find f’ in terms of g’. f(x)=x^2 g(x)

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