`f(x) = tanh(4x^2+3x)` Find the derivative of the function

Thursday, January 12, 2012

$\displaystyle{f{{\left({x}\right)}}}={\tanh{{\left({4}{{x}}^{{2}}+{3}{x}\right)}}}$ Find the derivative of the function

$\displaystyle{f{{\left({x}\right)}}}={\tanh{{\left({4}{{x}}^{{2}}+{3}{x}\right)}}}$

The derivative formula of hyperbolic tangent is

$\displaystyle\frac{{d}}{{\left.{d}{x}}}{\left[{\tanh{{\left({u}\right)}}}\right]}={{\sec{{h}}}}^{{2}}{\left({u}\right)}\cdot\frac{{{d}{u}}}{{\left.{d}{x}}}$

Applying this formula, the derivative of the function will be

$\displaystyle{f{'}}{\left({x}\right)}=\frac{{d}}{{\left.{d}{x}}}{\left[{\tanh{{\left({4}{{x}}^{{2}}+{3}{x}\right)}}}\right]}$

$\displaystyle{f{'}}{\left({x}\right)}={s}{e}{c}{{h}}^{{2}}{\left({4}{{x}}^{{2}}+{3}{x}\right)}\cdot\frac{{d}}{{\left.{d}{x}}}{\left({4}{{x}}^{{2}}+{3}{x}\right)}$

$\displaystyle{f{'}}{\left({x}\right)}={{\sec{{h}}}}^{{2}}{\left({4}{{x}}^{{2}}+{3}{x}\right)}\cdot{\left({8}{x}+{3}\right)}$

$\displaystyle{f{'}}{\left({x}\right)}={\left({8}{x}+{3}\right)}{{\sec{{h}}}}^{{2}}{\left({4}{{x}}^{{2}}+{3}{x}\right)}$

Therefore, the derivative of the given function is $\displaystyle{f{'}}{\left({x}\right)}={\left({8}{x}+{3}\right)}{{\sec{{h}}}}^{{2}}{\left({4}{{x}}^{{2}}+{3}{x}\right)}$ .

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Thursday, January 12, 2012

$\displaystyle{f{{\left({x}\right)}}}={\tanh{{\left({4}{{x}}^{{2}}+{3}{x}\right)}}}$ Find the derivative of the function

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Thomas Jefferson's election in 1800 is sometimes called the Revolution of 1800. Why could it be described in this way?

Thursday, January 12, 2012

Find the derivative of the function

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Post a Comment

Thomas Jefferson&#39;s election in 1800 is sometimes called the Revolution of 1800. Why could it be described in this way?

$\displaystyle{f{{\left({x}\right)}}}={\tanh{{\left({4}{{x}}^{{2}}+{3}{x}\right)}}}$ Find the derivative of the function

Thomas Jefferson's election in 1800 is sometimes called the Revolution of 1800. Why could it be described in this way?