What is the derivative of sqrt(log_{3)(x}*(x^3+2)) ?

The derivative of sqrt(log_{3)(x}*(x^3+2)) is (x^3+2+6x^3ln(x))/(2ln(3)xsqrt(log_{3)(x))}

What is the first derivative of sqrt(log_{3)(x}*(x^3+2)) ?

The first derivative of sqrt(log_{3)(x}*(x^3+2)) is (x^3+2+6x^3ln(x))/(2ln(3)xsqrt(log_{3)(x))}

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\frac{d}{d x} (lo g_{3} (x) \cdot (x^{3} + 2))

\frac{x ^{3} + 2 + 6 x ^{3} ln ( x )}{2 ln ( 3 ) x lo g _{3} ( x )}

Solution steps

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

Apply the Product Rule:

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

f = lo g_{3} (x), g = x^{3} + 2

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

\frac{d}{d x} (lo g_{3} (x)) = \frac{1}{2 ln ( 3 ) x lo g _{3} ( x )}

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

= \frac{1}{2 ln ( 3 ) x lo g _{3} ( x )} (x^{3} + 2) + 3 x^{2} lo g_{3} (x)

Simplify

\frac{1}{2 ln ( 3 ) x lo g _{3} ( x )} (x^{3} + 2) + 3 x^{2} lo g_{3} (x) : \frac{x ^{3} + 2 + 6 x ^{3} ln ( x )}{2 ln ( 3 ) x lo g _{3} ( x )}

= \frac{x ^{3} + 2 + 6 x ^{3} ln ( x )}{2 ln ( 3 ) x lo g _{3} ( x )}

What is the derivative of sqrt(log_{3)(x}*(x^3+2)) ?
The derivative of sqrt(log_{3)(x}*(x^3+2)) is (x^3+2+6x^3ln(x))/(2ln(3)xsqrt(log_{3)(x))}
What is the first derivative of sqrt(log_{3)(x}*(x^3+2)) ?
The first derivative of sqrt(log_{3)(x}*(x^3+2)) is (x^3+2+6x^3ln(x))/(2ln(3)xsqrt(log_{3)(x))}