Solve k*16x^4-8x^2+1

$$k \cdot 16 x ^ { 4 } - 8 x ^ { 2 } + 1$$

Differentiate w.r.t. x

$$64kx^{3}-16x$$

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}.

$$2\left(-8\right)x^{2-1}+4\times 16kx^{4-1}$$

Multiply 2 times -8.

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

Subtract 1 from 2.

$$-16x^{1}+4\times 16kx^{4-1}$$

Multiply 4 times 16k.

$$-16x^{1}+64kx^{4-1}$$

Subtract 1 from 4.

$$-16x^{1}+64kx^{3}$$

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

$$-16x+64kx^{3}$$

Evaluate

$$16kx^{4}-8x^{2}+1$$