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

The derivative of (3x^2+5x+1^{3/2}) is (3(6x+5)(3x^2+5x+1)^{1/2})/2

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

The first derivative of (3x^2+5x+1^{3/2}) is (3(6x+5)(3x^2+5x+1)^{1/2})/2

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

\frac{3 ( 6 x + 5 ) ( 3 x ^{2} + 5 x + 1 ) ^{\frac{1}{2}}}{2}

Solution steps

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

Apply the chain rule:

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

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

\frac{d}{d x} (3 x^{2} + 5 x + 1) = 6 x + 5

= \frac{3 ( 3 x ^{2} + 5 x + 1 ) ^{\frac{1}{2}}}{2} (6 x + 5)

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{3 ( 6 x + 5 ) ( 3 x ^{2} + 5 x + 1 ) ^{\frac{1}{2}}}{2}

f (x) = lo g_{41} (2 x - 4)

\frac{d}{d x} (ln (x) cos (x))

x^{2} y^{^{''}} + 3 x y^{^{'}} - 15 y = 0

\frac{6}{s ^{2} + 5 s + 6}

x \to 4 lim (\frac{x ^{2} + x}{x + 1})

What is the derivative of (3x^2+5x+1^{3/2}) ?
The derivative of (3x^2+5x+1^{3/2}) is (3(6x+5)(3x^2+5x+1)^{1/2})/2
What is the first derivative of (3x^2+5x+1^{3/2}) ?
The first derivative of (3x^2+5x+1^{3/2}) is (3(6x+5)(3x^2+5x+1)^{1/2})/2