What is the derivative of 10xlog_{10}(100x) ?

The derivative of 10xlog_{10}(100x) is 10(log_{10}(x)+2+1/(ln(10)))

What is the first derivative of 10xlog_{10}(100x) ?

The first derivative of 10xlog_{10}(100x) is 10(log_{10}(x)+2+1/(ln(10)))

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\frac{d}{d x} (10 x lo g_{10} (100 x))

10 (lo g_{10} (x) + 2 + \frac{1}{ln ( 10 )})

Solution steps

\frac{d}{d x} (10 x lo g_{10} (100 x))

Simplify

10 x lo g_{10} (100 x) : 10 x (lo g_{10} (x) + 2)

= \frac{d}{d x} (10 x (lo g_{10} (x) + 2))

Take the constant out:

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

= 10 \frac{d}{d x} (x (lo g_{10} (x) + 2))

Apply the Product Rule:

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

f = x, g = lo g_{10} (x) + 2

= 10 (\frac{d x}{d x} (lo g_{10} (x) + 2) + \frac{d}{d x} (lo g_{10} (x) + 2) x)

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

\frac{d}{d x} (lo g_{10} (x) + 2) = \frac{1}{ln ( 10 ) x}

= 10 (1 \cdot (lo g_{10} (x) + 2) + \frac{1}{ln ( 10 ) x} x)

Simplify

10 (1 \cdot (lo g_{10} (x) + 2) + \frac{1}{ln ( 10 ) x} x) : 10 (lo g_{10} (x) + 2 + \frac{1}{ln ( 10 )})

= 10 (lo g_{10} (x) + 2 + \frac{1}{ln ( 10 )})

ln (y)

y = x^{2} sin^{7} (x) + x cos^{- 6} (x)

\int \frac{1}{- 20 x - 20 x} d x

x y^{^{'}} + (1 + 2 x^{2}) y = x^{3} e^{- x^{2}}

\frac{d}{d x} (sec (7 x))

What is the derivative of 10xlog_{10}(100x) ?
The derivative of 10xlog_{10}(100x) is 10(log_{10}(x)+2+1/(ln(10)))
What is the first derivative of 10xlog_{10}(100x) ?
The first derivative of 10xlog_{10}(100x) is 10(log_{10}(x)+2+1/(ln(10)))