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1

Ejemplo

$\frac{d}{dx}\left(\left(4x^2+3\right)^7\right)$
2

The power rule for differentiation states that if $n$ is a real number and $f(x) = x^n$, then $f'(x) = nx^{n-1}$

$7\left(3+4x^2\right)^{6}\cdot\frac{d}{dx}\left(3+4x^2\right)$
3

The derivative of a sum of two functions is the sum of the derivatives of each function

$7\left(3+4x^2\right)^{6}\left(\frac{d}{dx}\left(3\right)+\frac{d}{dx}\left(4x^2\right)\right)$
4

The derivative of the constant function is equal to zero

$7\left(3+4x^2\right)^{6}\left(0+\frac{d}{dx}\left(4x^2\right)\right)$
5

The derivative of a function multiplied by a constant is equal to the constant times the derivative of the function

$7\left(3+4x^2\right)^{6}\left(0+4\frac{d}{dx}\left(x^2\right)\right)$
6

The power rule for differentiation states that if $n$ is a real number and $f(x) = x^n$, then $f'(x) = nx^{n-1}$

$7\left(3+4x^2\right)^{6}\left(0+8x\right)$
7

$x+0=x$, where $x$ is any expression

$56\left(3+4x^2\right)^{6}x$