What is the derivative of (5x^2-x+11)^{3/2} ?

The derivative of (5x^2-x+11)^{3/2} is (3(10x-1)(5x^2-x+11)^{1/2})/2

What is the first derivative of (5x^2-x+11)^{3/2} ?

The first derivative of (5x^2-x+11)^{3/2} is (3(10x-1)(5x^2-x+11)^{1/2})/2

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derivative of

(5 x^{2} - x + 11)^{\frac{3}{2}}

\frac{3 ( 10 x - 1 ) ( 5 x ^{2} - x + 11 ) ^{\frac{1}{2}}}{2}

Solution steps

\frac{d}{d x} ((5 x^{2} - x + 11)^{\frac{3}{2}})

Apply the chain rule:

\frac{3 ( 5 x ^{2} - x + 11 ) ^{\frac{1}{2}}}{2} \frac{d}{d x} (5 x^{2} - x + 11)

= \frac{3 ( 5 x ^{2} - x + 11 ) ^{\frac{1}{2}}}{2} \frac{d}{d x} (5 x^{2} - x + 11)

\frac{d}{d x} (5 x^{2} - x + 11) = 10 x - 1

= \frac{3 ( 5 x ^{2} - x + 11 ) ^{\frac{1}{2}}}{2} (10 x - 1)

Multiply fractions:

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

= \frac{3 ( 10 x - 1 ) ( 5 x ^{2} - x + 11 ) ^{\frac{1}{2}}}{2}

4 y^{^{''}} - 4 y^{^{'}} + y = 16 e^{\frac{t}{2}}

f (x) = 3 e^{x} + 2 x, (0, 3)

x \to 0 lim (\frac{1}{x ^{3}})

x \to 0 + lim (x^{17 x})

\int_{0}^{5} x e^{- x^{2}} d x

What is the derivative of (5x^2-x+11)^{3/2} ?
The derivative of (5x^2-x+11)^{3/2} is (3(10x-1)(5x^2-x+11)^{1/2})/2
What is the first derivative of (5x^2-x+11)^{3/2} ?
The first derivative of (5x^2-x+11)^{3/2} is (3(10x-1)(5x^2-x+11)^{1/2})/2