Ans

 

 

 

 

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Find \displaystyle \frac{dy}{dx}:

    \[y=5x^{3}+7x^{2}-6x+11\]

Source: Schwartz, A. (1960). Analytic Geometry and Calculus. New York: Holt, Rinehart and Winston. (Question 1(a): Exercises 1.6, p. 30)

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Find \displaystyle \frac{dy}{dx}:

    \[y=20x^{5}+6x^{3}+7x-\sqrt{11}\]

Source: Schwartz, A. (1960). Analytic Geometry and Calculus. New York: Holt, Rinehart and Winston. (Question 1(b): Exercises 1.6, p. 30)

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Find \displaystyle \frac{du}{dx}:

    \[u=ax^{2}+bx+c\]

Source: Schwartz, A. (1960). Analytic Geometry and Calculus. New York: Holt, Rinehart and Winston. (Question 1(c): Exercises 1.6, p. 30)

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Find \displaystyle \frac{dy}{dx}:

    \[v=4+5x^{2}+12x^{4}\]

Source: Schwartz, A. (1960). Analytic Geometry and Calculus. New York: Holt, Rinehart and Winston. (Question 1(d): Exercises 1.6, p. 30)

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Find \displaystyle \frac{dS}{dr}:

    \[S=4 \pi r^{2}\]

Source: Schwartz, A. (1960). Analytic Geometry and Calculus. New York: Holt, Rinehart and Winston. (Question 1(e): Exercises 1.6, p. 31)

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Find \displaystyle \frac{dx}{dt}:

    \[V=\frac{4}{3} \pi r^{3}\]

Source: Schwartz, A. (1960). Analytic Geometry and Calculus. New York: Holt, Rinehart and Winston. (Question 1(f): Exercises 1.6, p. 31)

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Find \displaystyle \frac{dx}{dt}:

    \[x=\frac{2}{t}+\frac{3}{t^{2}}\]

Source: Schwartz, A. (1960). Analytic Geometry and Calculus. New York: Holt, Rinehart and Winston. (Question 1(g): Exercises 1.6, p. 31)

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Find \displaystyle \frac{dx}{dt}:

    \[T=2u^{2}+u-4+\frac{3}{u}-\frac{7}{u^{2}}\]

Source: Schwartz, A. (1960). Analytic Geometry and Calculus. New York: Holt, Rinehart and Winston. (Question 1(h): Exercises 1.6, p. 31)

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Find \displaystyle \frac{dx}{dt}:

    \[y=\frac{2r^{2}+4}{r}\]

Source: Schwartz, A. (1960). Analytic Geometry and Calculus. New York: Holt, Rinehart and Winston. (Question 1(i): Exercises 1.6, p. 31)

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Find \displaystyle \frac{dx}{dt}:

    \[L=\left(az^{2}+b\right)\left(z-c\right)\]

Source: Schwartz, A. (1960). Analytic Geometry and Calculus. New York: Holt, Rinehart and Winston. (Question 1(j): Exercises 1.6, p. 31)

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Find \displaystyle \frac{dx}{dt}:

    \[Q=\frac{\left(x^{2}+2\right)\left(x-5\right)}{\sqrt{x}}\]

Source: Schwartz, A. (1960). Analytic Geometry and Calculus. New York: Holt, Rinehart and Winston. (Question 1(k): Exercises 1.6, p. 31)

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Find \displaystyle \frac{dx}{dt}:

    \[f\left(x\right)=2x^{3}-17x^{2}-5\]

Source: Schwartz, A. (1960). Analytic Geometry and Calculus. New York: Holt, Rinehart and Winston. (Question 1(l): Exercises 1.6, p. 31)

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Find \displaystyle \frac{dx}{dt}:

    \[\phi\left(t\right)=3x^{2}+\sqrt{t}\]

Source: Schwartz, A. (1960). Analytic Geometry and Calculus. New York: Holt, Rinehart and Winston. (Question 1(m), Exercises 1.6, p. 31)

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Find \displaystyle \frac{dx}{dt}:

    \[y=6\sqrt{x}+3\sqrt[3]{x}\]

Source: Schwartz, A. (1960). Analytic Geometry and Calculus. New York: Holt, Rinehart and Winston. (Question 1(n): Exercises 1.6, p. 31)

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Find \displaystyle \frac{dx}{dt}:

    \[H=2\sqrt{x^{3}}-5\sqrt[3]{x^{2}}\]

Source: Schwartz, A. (1960). Analytic Geometry and Calculus. New York: Holt, Rinehart and Winston. (Question 1(o): Exercises 1.6, p. 31)

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Find \displaystyle \frac{dx}{dt}:

    \[f\left(t\right)=\frac{16}{\sqrt[4]{t^{3}}}\]

Source: Schwartz, A. (1960). Analytic Geometry and Calculus. New York: Holt, Rinehart and Winston. (Question 1(p): Exercises 1.6, p. 31)

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Find \displaystyle \frac{dx}{dt}:

    \[P=\frac{k}{V^{1.4}}\]

Source: Schwartz, A. (1960). Analytic Geometry and Calculus. New York: Holt, Rinehart and Winston. (Question 1(q): Exercises 1.6, p. 31)

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Author: ascklee

Dr. Lee teaches at the Wee Kim Wee School of Communication and Information at the Nanyang Technological University in Singapore. He founded The Mathematics Digital Library in 2013.

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