What is the derivative of 5sqrt(3x^3+x) ?

The derivative of 5sqrt(3x^3+x) is (5(9x^2+1))/(2sqrt(3x^3+x))

What is the first derivative of 5sqrt(3x^3+x) ?

The first derivative of 5sqrt(3x^3+x) is (5(9x^2+1))/(2sqrt(3x^3+x))

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derivative of

5 3 x^{3} + x

\frac{5 ( 9 x ^{2} + 1 )}{2 3 x ^{3} + x}

Solution steps

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

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply the chain rule:

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

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

\frac{d}{d x} (3 x^{3} + x) = 9 x^{2} + 1

= 5 \cdot \frac{1}{2 3 x ^{3} + x} (9 x^{2} + 1)

Simplify

5 \cdot \frac{1}{2 3 x ^{3} + x} (9 x^{2} + 1) : \frac{5 ( 9 x ^{2} + 1 )}{2 3 x ^{3} + x}

= \frac{5 ( 9 x ^{2} + 1 )}{2 3 x ^{3} + x}

\frac{e ^{\frac{1}{x}}}{x ^{3}}

f (x) = x + 1, (3, 2)

\int C e^{- a t} d t

f (x) = \frac{6}{x ^{4}}

y^{^{'}} = \frac{x + 2 y}{x}

What is the derivative of 5sqrt(3x^3+x) ?
The derivative of 5sqrt(3x^3+x) is (5(9x^2+1))/(2sqrt(3x^3+x))
What is the first derivative of 5sqrt(3x^3+x) ?
The first derivative of 5sqrt(3x^3+x) is (5(9x^2+1))/(2sqrt(3x^3+x))