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Chapter 4: Q. 37 (page 399)

Use the Second Fundamental Theorem of Calculus, if needed, to calculate each the derivatives expressed in Exercises 35鈥�48.
ddx鈭�0x2cost.dt

Short Answer

Expert verified

The derivative expression of ddx鈭�0x2cost.dtis cosx2(2x).

Step by step solution

01

Step 1. Given Information.

The derivative:

ddx鈭�0x2cost.dt

02

Step 2. Second Fundamental theorem of calculus.

f is continuous on [a,b]for all x鈭�[a,b], thenddx鈭�eu(x)f(t).dt=f(u(x))u'(x)

03

Step 3. Find the derivative expression.

By Second Fundamental theorem of calculus,

ddx鈭�0x2cost.dt=cosx2(x2)'=cosx2(2x)

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