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Chapter 4: Q. 35 (page 399)

Use the Second Fundamental Theorem of Calculus, if needed, to calculate each the derivatives expressed in Exercises 35鈥�48.

ddx鈭�x4et2+1.dt

Short Answer

Expert verified

The derivative expression of ddx鈭�x4et2+1.dtis -ex2+1.

Step by step solution

01

Step 1. Given Information.

The derivative:

ddx鈭�x4et2+1.dt

02

Step 2. Second Fundamental theorem of calculus.

f is continuous on [a,b]for all x鈭�[a,b], then

ddx鈭�exf(t).dt=f(x).

03

Step 3. Find the derivative expression.

By Second Fundamental theorem of calculus,

ddx鈭�x4et2+1.dt=ddx-鈭�4xet2+1.dt=-ex2+1

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