Solve (2x^5-4x^4+3x^2-4)^prime

$$( 2 x ^ { 5 } - 4 x ^ { 4 } + 3 x ^ { 2 } - 4 ) ^ { \prime }$$

Evaluate

$$10x^{4}-16x^{3}+6x$$

Steps Using Derivative Rule for Sum

The derivative of a polynomial is the sum of the derivatives of its terms. The derivative of a constant term is 0. The derivative of ax^{n} is nax^{n-1}.

$$5\times 2x^{5-1}+4\left(-4\right)x^{4-1}+2\times 3x^{2-1}$$

Multiply 5 times 2.

$$10x^{5-1}+4\left(-4\right)x^{4-1}+2\times 3x^{2-1}$$

Subtract 1 from 5.

$$10x^{4}+4\left(-4\right)x^{4-1}+2\times 3x^{2-1}$$

Multiply 4 times -4.

$$10x^{4}-16x^{4-1}+2\times 3x^{2-1}$$

Subtract 1 from 4.

$$10x^{4}-16x^{3}+2\times 3x^{2-1}$$

Multiply 4 times -4.

$$10x^{4}-16x^{3}+6x^{2-1}$$

Subtract 1 from 2.

$$10x^{4}-16x^{3}+6x^{1}$$

For any term t, t^{1}=t.

$$10x^{4}-16x^{3}+6x$$

Differentiate w.r.t. x

$$40x^{3}-48x^{2}+6$$