What is the derivative of (log_{10}(6*x^2)^3) ?

The derivative of (log_{10}(6*x^2)^3) is 6log_{10}(6)^3x^5

What is the first derivative of (log_{10}(6*x^2)^3) ?

The first derivative of (log_{10}(6*x^2)^3) is 6log_{10}(6)^3x^5

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\frac{d}{d x} ((lo g_{10} (6) \cdot x^{2})^{3})

6 lo g_{10} (6)^{3} x^{5}

Solution steps

\frac{d}{d x} ((lo g_{10} (6) x^{2})^{3})

Simplify

(lo g_{10} (6) x^{2})^{3} : lo g_{10} (6)^{3} x^{6}

= \frac{d}{d x} (lo g_{10} (6)^{3} x^{6})

Take the constant out:

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

= lo g_{10} (6)^{3} \frac{d}{d x} (x^{6})

Apply the Power Rule:

\frac{d}{d x} (x^{a}) = a \cdot x^{a - 1}

= lo g_{10} (6)^{3} \cdot 6 x^{6 - 1}

Simplify

= 6 lo g_{10} (6)^{3} x^{5}

(3 x^{2} - 5 x)^{45}

cos (2 x + 3)

(\frac{x}{3})^{2}

6 cos (x) + sin^{2} (x)

\frac{d}{d a} (cos^{4} (a) - sin^{4} (a) + 1)

What is the derivative of (log_{10}(6*x^2)^3) ?
The derivative of (log_{10}(6*x^2)^3) is 6log_{10}(6)^3x^5
What is the first derivative of (log_{10}(6*x^2)^3) ?
The first derivative of (log_{10}(6*x^2)^3) is 6log_{10}(6)^3x^5