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Popular >

derivative of xsqrt(4+3x^3)

Solution

\frac{d}{d x} (x 4 + 3 x^{3})

Solution

\frac{15 x ^{3} + 8}{2 4 + 3 x ^{3}}

Solution steps

\frac{d}{d x} (x 4 + 3 x^{3})

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x, g = 4 + 3 x^{3}

= \frac{d x}{d x} 4 + 3 x^{3} + \frac{d}{d x} (4 + 3 x^{3}) x

\frac{d x}{d x} = 1

\frac{d}{d x} (4 + 3 x^{3}) = \frac{9 x ^{2}}{2 4 + 3 x ^{3}}

= 1 \cdot 4 + 3 x^{3} + \frac{9 x ^{2}}{2 4 + 3 x ^{3}} x

Simplify

1 \cdot 4 + 3 x^{3} + \frac{9 x ^{2}}{2 4 + 3 x ^{3}} x : \frac{15 x ^{3} + 8}{2 4 + 3 x ^{3}}

= \frac{15 x ^{3} + 8}{2 4 + 3 x ^{3}}

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Frequently Asked Questions (FAQ)

What is the derivative of xsqrt(4+3x^3) ?
The derivative of xsqrt(4+3x^3) is (15x^3+8)/(2sqrt(4+3x^3))
What is the first derivative of xsqrt(4+3x^3) ?
The first derivative of xsqrt(4+3x^3) is (15x^3+8)/(2sqrt(4+3x^3))