What is the derivative of 1000^{log_{10}(x)} ?

The derivative of 1000^{log_{10}(x)} is (3*1000^{log_{10}(x)})/x

What is the first derivative of 1000^{log_{10}(x)} ?

The first derivative of 1000^{log_{10}(x)} is (3*1000^{log_{10}(x)})/x

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derivative of

100 0^{l o g_{10} (x)}

\frac{3 \cdot 100 0 ^{l o g_{10} (x)}}{x}

Solution steps

\frac{d}{d x} (100 0^{l o g_{10} (x)})

Apply exponent rule:

a^{b} = e^{b l n (a)}

100 0^{l o g_{10} (x)} = e^{l o g_{10} (x) l n (1000)}

= \frac{d}{d x} (e^{l o g_{10} (x) l n (1000)})

Apply the chain rule:

e^{l o g_{10} (x) l n (1000)} \frac{d}{d x} (lo g_{10} (x) ln (1000))

= e^{l o g_{10} (x) l n (1000)} \frac{d}{d x} (lo g_{10} (x) ln (1000))

\frac{d}{d x} (lo g_{10} (x) ln (1000)) = \frac{3}{x}

= e^{l o g_{10} (x) l n (1000)} \frac{3}{x}

Simplify

e^{l o g_{10} (x) l n (1000)} \frac{3}{x} : \frac{3 \cdot 100 0 ^{l o g_{10} (x)}}{x}

= \frac{3 \cdot 100 0 ^{l o g_{10} (x)}}{x}

\int \frac{x ^{2} - 4 x + 4}{x ^{2} - 4 x + 40} d x

ln (ln (ln (x)))

\frac{d ^{3}}{d x ^{3}} (\frac{9}{x})

2 \frac{d ^{2} y}{d x ^{2}} + 32 y = 0

\int - \frac{1}{4 x} d x

What is the derivative of 1000^{log_{10}(x)} ?
The derivative of 1000^{log_{10}(x)} is (3*1000^{log_{10}(x)})/x
What is the first derivative of 1000^{log_{10}(x)} ?
The first derivative of 1000^{log_{10}(x)} is (3*1000^{log_{10}(x)})/x