Expand each function (using the appropiate technique/formula) Compute the derivative of the expanded function by applying the differentiation rules f(x)=(x+5)2 f(x)=(4x2−3)2

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Expand each function (using the appropiate technique/formula) Compute the derivative of the expanded function by applying the differentiation rules  f(x)=(x+5)2  f(x)=(4x2−3)2

kaluitagf · Accepted Answer

Step 1: To determine  Derivative of the given functions by expanding them:  1) f(x)=(x+5)2  2) f(x)=(4x2−3)2  Step 2: Formula used  1. (x+y)2=x2+2xy+y2  2. (x−y)2=x2−xy+y2  3. ddx(xn)=nxn−1  Step 3: Solution  Consider the given function:  f(x)=(x+5)2  Using formula, the expanded function is given by:  f(x)=x2+2.x.5+52  ⇒f(x)=x2+10x+25  Differentiating the above function with respect to x, we get,  df(x)dx=ddx∣(x2+10x+25)  ⇒df(x)dx=ddx(x2)+ddx(10x)+ddx(25)  ⇒df(x)dx=2x+10(1)+0  ⇒df(x)dx=2x+10  Hence, the derivative of the given function is dfdx=2x+10

Chanell Sanborn · Accepted Answer

Step 4  Consider the given function:  f(x)=(4x2−3)2  Using formula, the expanded function is given by:  f(x)=(4x2)2−2.(4x2)(3)+32  ⇒f(x)=16x4−24x2+9  Differentiating the above function with respect to x, we get,  df(x)dx=ddx(16x4−24x2+9)  ⇒df(x)dx=ddx(16x4)+ddx(−24x2)+ddx(9)  ⇒df(x)dx=16ddx(x4)−24ddx(x2)+ddx(9)  ⇒df(x)dx=16(4x3)−24(2x)+(0)  ⇒df(x)dx=64x3−48x  Hence, the derivative of the given function is dfdx=64x3−48x

Expand each function (using the appropiate technique/formula) Compute the derivative

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