What is the derivative of $10 x$ $10x$ ?

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What is the derivative of $10 x$ $10x$ ?

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Answer 1 · 2015-06-22T10:23:19

The derivative of 10x with respect to x is 10.

Explanation:

Let

$y = 10 x$ $y=10x$

Differentiate $y$ $y$ with respect to $x$ $x$ .

$\frac{d y}{d x} = \frac{d}{d x} (10 x)$ $(dy)/(dx)=d/(dx)(10x)$

$\frac{d y}{d x} = x \frac{d}{d x} (10) + 10 \frac{d}{d x} (x)$ $(dy)/(dx)=xd/(dx)(10)+10d/(dx)(x)$ [since $\frac{d}{d x} (u v) = u \frac{d}{d x} v + v \frac{d}{d x} u]$ $d/(dx)(uv)=ud/(dx)v+vd/(dx)u]$

$\frac{d y}{d x} = x (0) + 10 (1)$ $(dy)/(dx)=x(0)+10(1)$ [ $\frac{d}{d x} (c o n s t) = 0; \frac{d}{d x} (x) = 1]$ $d/(dx)(const)=0;d/(dx)(x)=1]$

$\frac{d y}{d x} = 10$ $(dy)/(dx)=10$

The derivative of 10x with respect to x is 10.

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What is the derivative of $10 x$ $10x$ ?

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