What is the derivative of (14+5x-3x^2^{3/4}) ?

The derivative of (14+5x-3x^2^{3/4}) is (3(-6x+5))/(4(14+5x-3x^2)^{1/4)}

What is the first derivative of (14+5x-3x^2^{3/4}) ?

The first derivative of (14+5x-3x^2^{3/4}) is (3(-6x+5))/(4(14+5x-3x^2)^{1/4)}

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\frac{d}{d x} ((14 + 5 x - 3 x^{2})^{\frac{3}{4}})

\frac{3 ( - 6 x + 5 )}{4 ( 14 + 5 x - 3 x ^{2} ) ^{\frac{1}{4}}}

Solution steps

\frac{d}{d x} ((14 + 5 x - 3 x^{2})^{\frac{3}{4}})

Apply the chain rule:

\frac{3}{4 ( 14 + 5 x - 3 x ^{2} ) ^{\frac{1}{4}}} \frac{d}{d x} (14 + 5 x - 3 x^{2})

= \frac{3}{4 ( 14 + 5 x - 3 x ^{2} ) ^{\frac{1}{4}}} \frac{d}{d x} (14 + 5 x - 3 x^{2})

\frac{d}{d x} (14 + 5 x - 3 x^{2}) = - 6 x + 5

= \frac{3}{4 ( 14 + 5 x - 3 x ^{2} ) ^{\frac{1}{4}}} (- 6 x + 5)

Multiply fractions:

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

= \frac{3 ( - 6 x + 5 )}{4 ( 14 + 5 x - 3 x ^{2} ) ^{\frac{1}{4}}}

What is the derivative of (14+5x-3x^2^{3/4}) ?
The derivative of (14+5x-3x^2^{3/4}) is (3(-6x+5))/(4(14+5x-3x^2)^{1/4)}
What is the first derivative of (14+5x-3x^2^{3/4}) ?
The first derivative of (14+5x-3x^2^{3/4}) is (3(-6x+5))/(4(14+5x-3x^2)^{1/4)}