What is the derivative of 1/3 (x^2+2^{3/2}-5) ?

The derivative of 1/3 (x^2+2^{3/2}-5) is x(x^2+2)^{1/2}

What is the first derivative of 1/3 (x^2+2^{3/2}-5) ?

The first derivative of 1/3 (x^2+2^{3/2}-5) is x(x^2+2)^{1/2}

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\frac{d}{d x} (\frac{1}{3} (x^{2} + 2)^{\frac{3}{2}} - 5)

x (x^{2} + 2)^{\frac{1}{2}}

Solution steps

\frac{d}{d x} (\frac{1}{3} (x^{2} + 2)^{\frac{3}{2}} - 5)

Simplify

\frac{1}{3} (x^{2} + 2)^{\frac{3}{2}} - 5 : \frac{( x ^{2} + 2 ) ^{\frac{3}{2}}}{3} - 5

= \frac{d}{d x} \frac{( x ^{2} + 2 ) ^{\frac{3}{2}}}{3} - 5

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d x} \frac{( x ^{2} + 2 ) ^{\frac{3}{2}}}{3} - \frac{d}{d x} (5)

\frac{d}{d x} \frac{( x ^{2} + 2 ) ^{\frac{3}{2}}}{3} = x (x^{2} + 2)^{\frac{1}{2}}

\frac{d}{d x} (5) = 0

= x (x^{2} + 2)^{\frac{1}{2}} - 0

Simplify

= x (x^{2} + 2)^{\frac{1}{2}}

\frac{d}{d x} (\frac{1}{sec ^{2} ( x )})

f (x) = \frac{2}{x + 1}, at x = 7

x \to 0 + lim (\frac{12}{x ^{2}})

\int_{0}^{2} \frac{x ^{2}}{2} d x

\int \frac{3}{4 x - x ^{2}} d x

What is the derivative of 1/3 (x^2+2^{3/2}-5) ?
The derivative of 1/3 (x^2+2^{3/2}-5) is x(x^2+2)^{1/2}
What is the first derivative of 1/3 (x^2+2^{3/2}-5) ?
The first derivative of 1/3 (x^2+2^{3/2}-5) is x(x^2+2)^{1/2}