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CALCULUS AND ANALYSIS
DIFFERENTIAL CALCULUS
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Differential Calculus answers
Recent questions in Differential Calculus
Derivatives
asked 2021-05-19
Find the four second partial derivatives of the following functions.
\(\displaystyle{F}{\left({r},{s}\right)}={r}{e}^{{{s}}}\)
Derivatives
asked 2021-05-16
Find the first partial derivatives of the following functions.
\(\displaystyle{h}{\left({x},{y}\right)}={x}-\sqrt{{{x}^{{{2}}}-{4}{y}}}\)
Derivatives
asked 2021-05-16
Find the partial derivatives:
\(\displaystyle{f{{\left({x},{y}\right)}}}={7}{x}^{{{7}\cdot{4}}}{y}^{{{3}}}+{z}^{{{3}}}\)
\(\displaystyle{\frac{{\partial{f}}}{{\partial{x}}}}=\)
?
\(\displaystyle{\frac{{\partial{f}}}{{\partial{y}}}}=\)
?
\(\displaystyle{\frac{{\partial{f}}}{{\partial{z}}}}=\)
?
Derivatives
asked 2021-05-09
Find both first partial derivatives.
\(\displaystyle{f{{\left({x},{y}\right)}}}={4}{x}^{{{3}}}{y}-{2}\)
Derivatives
asked 2021-05-09
Find all first partial derivatives of the following function.
\(\displaystyle{f{{\left({x},{y}\right)}}}={y}{\cos{{\left({x}^{{{2}}}+{y}^{{{2}}}\right)}}}\)
Derivatives
asked 2021-05-08
find the indicated derivatives.
\(\displaystyle{\frac{{{d}{s}}}{{{\left.{d}{t}\right.}}}}{\quad\text{if}\quad}{s}={\frac{{{t}}}{{{2}{t}+{1}}}}\)
.
Derivatives
asked 2021-05-04
Find the derivatives of the following functions.
\(\displaystyle{f{{\left({x}\right)}}}={x}{\tan{{h}}}{x}\)
Derivatives
asked 2021-05-04
Find the derivatives of the following functions.
\(\displaystyle{f{{\left({v}\right)}}}={{\sin{{h}}}^{{-{1}}}{v}^{{{2}}}}\)
Derivatives
asked 2021-05-03
Find the derivatives.
\(\displaystyle{y}={\left({x}^{{{2}}}+{6}{x}+{2}\right)}{\left({\frac{{{2}}}{{{x}^{{{4}}}}}}+\sqrt{{{3}}}{\left\lbrace{x}^{{{5}}}\right\rbrace}+{3}\right)}\)
Derivatives
asked 2021-04-30
Derivatives of the sum of functions Find the derivative of the following functions.
\(\displaystyle{f{{\left({x}\right)}}}={3}{x}^{{{4}}}+{7}{x}\)
Derivatives
asked 2021-04-28
Find the
\(\displaystyle{100}^{{{t}{h}}}\)
derivative of
\(\displaystyle{y}={e}^{{{x}}}\)
Derivatives
asked 2021-04-27
find the indicated derivatives.
\(\displaystyle{\frac{{{\left.{d}{y}\right.}}}{{{\left.{d}{x}\right.}}}}{\quad\text{if}\quad}{y}={2}{x}^{{{3}}}\)
Derivatives
asked 2021-04-26
Find both first partial derivatives.
\(\displaystyle{z}={\cos{{x}}}{y}\)
Derivatives
asked 2021-04-25
Find both first partial derivatives.
\(\displaystyle{z}={\sin{{h}}}{\left({2}{x}+{3}{y}\right)}\)
Derivatives
asked 2021-04-24
Find the second partial derivatives for the function
\(\displaystyle{f{{\left({x},{y}\right)}}}={x}^{{{4}}}-{3}{x}^{{{2}}}{y}^{{{2}}}+{y}^{{{2}}}\)
and evaluate it at the point(1,0).
Derivatives
asked 2021-04-23
Chain Rule and Higher Order Derivatives. Find the derivative
\(\displaystyle{f{{\left({x}\right)}}}={\left({5}{x}^{{{2}}}-{2}{x}+{1}\right)}^{{{3}}}\)
Derivatives
asked 2021-04-23
Using the Extended Power Rule Find the following derivatives.
\(\displaystyle{\frac{{{d}}}{{{\left.{d}{x}\right.}}}}{\left({\frac{{{9}}}{{{x}^{{{5}}}}}}\right)}\)
Derivatives
asked 2021-04-20
Find the indicated derivatives.
\(\displaystyle{\frac{{{d}{s}}}{{{\left.{d}{t}\right.}}}}{\quad\text{if}\quad}{s}={\frac{{{t}}}{{{2}{t}+{1}}}}\)
Derivatives
asked 2021-04-20
The derivatives of
\(\displaystyle{{\sin}^{{-{1}}}{x}}{\quad\text{and}\quad}{{\cos}^{{-{1}}}{x}}\)
are negatives of each other.
Derivatives
asked 2021-04-19
Find both first partial derivatives.
\(\displaystyle{z}={\sin{{\left({5}{x}\right)}}}{\cos{{\left({5}{y}\right)}}}\)
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