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Derivatives: Chain Rule

Please see the attached file for the fully formatted problems. For a composite function f(x) = g(u(x)) state the chain rule for the derivative f(x). For each of the following functions, compute the derivative, simplifying your answers. f(x)=ln(1 + x^2) f(x)= sin(x^2) f(x) = (sin x)^2

Subject:

Math

Topic:

Calculus

Posting ID:

5312

OTA ID:

102523

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Evaluate integrals

Please see the attached file for the fully formatted problems. Evaluate the following integrals. S (4x^3 -2x - (2/x^3) dx S (1/2x^1/2) dx 1-->0 S ln x dx

Subject:

Math

Topic:

Calculus

Posting ID:

5313

OTA ID:

103059

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Rectilinear motion: Calculation of velocity

A billiard ball is hit and travels in a line. If s centimeters is the distance of the ball from its initial position at t seconds, then s=100t2 + 100t. If the ball hits a cushion that is 39cm from its initial position, at what velocity does it hit the cushion?

Subject:

Math

Topic:

Calculus

Posting ID:

5350

OTA ID:

103095

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Finding a tangent line to a curve.

Find an equation of the tangent line to the curve, Y = x^3 - 3x^2 + 5x that has the least slope.

Subject:

Math

Topic:

Calculus

Posting ID:

5394

OTA ID:

103570

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Differentiation: Shadow Shortening Problem

A man 6 ft tall is walking toward a building at the rate of 5 ft/sec. If there is a light on the ground 50 ft from the building, how fast is the man's shadow on the building growing shorter when he is 30ft from the building?

Subject:

Math

Topic:

Calculus

Posting ID:

5396

OTA ID:

103139

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