What is the derivative of 4x^5-3x^m+2x^n+5x^2-x-6 ?

The derivative of 4x^5-3x^m+2x^n+5x^2-x-6 is 20x^4+10x+2nx^{n-1}-3mx^{m-1}-1

What is the first derivative of 4x^5-3x^m+2x^n+5x^2-x-6 ?

The first derivative of 4x^5-3x^m+2x^n+5x^2-x-6 is 20x^4+10x+2nx^{n-1}-3mx^{m-1}-1

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\frac{d}{d x} (4 x^{5} - 3 x^{m} + 2 x^{n} + 5 x^{2} - x - 6)

20 x^{4} + 10 x + 2 n x^{n - 1} - 3 m x^{m - 1} - 1

Solution steps

\frac{d}{d x} (4 x^{5} - 3 x^{m} + 2 x^{n} + 5 x^{2} - x - 6)

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d x} (4 x^{5}) - \frac{d}{d x} (3 x^{m}) + \frac{d}{d x} (2 x^{n}) + \frac{d}{d x} (5 x^{2}) - \frac{d x}{d x} - \frac{d}{d x} (6)

\frac{d}{d x} (4 x^{5}) = 20 x^{4}

\frac{d}{d x} (3 x^{m}) = 3 m x^{m - 1}

\frac{d}{d x} (2 x^{n}) = 2 n x^{n - 1}

\frac{d}{d x} (5 x^{2}) = 10 x

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

\frac{d}{d x} (6) = 0

= 20 x^{4} - 3 m x^{m - 1} + 2 n x^{n - 1} + 10 x - 1 - 0

Simplify

= 20 x^{4} + 10 x + 2 n x^{n - 1} - 3 m x^{m - 1} - 1

What is the derivative of 4x^5-3x^m+2x^n+5x^2-x-6 ?
The derivative of 4x^5-3x^m+2x^n+5x^2-x-6 is 20x^4+10x+2nx^{n-1}-3mx^{m-1}-1
What is the first derivative of 4x^5-3x^m+2x^n+5x^2-x-6 ?
The first derivative of 4x^5-3x^m+2x^n+5x^2-x-6 is 20x^4+10x+2nx^{n-1}-3mx^{m-1}-1