Solve f(x)=-7x^4+8x^2-3x+5

$$f ( x ) = - 7 x ^ { 4 } + 8 x ^ { 2 } - 3 x + 5$$

Differentiate w.r.t. x

$$-28x^{3}+16x-3$$

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}.

$$4\left(-7\right)x^{4-1}+2\times 8x^{2-1}-3x^{1-1}$$

Multiply 4 times -7.

$$-28x^{4-1}+2\times 8x^{2-1}-3x^{1-1}$$

Subtract 1 from 4.

$$-28x^{3}+2\times 8x^{2-1}-3x^{1-1}$$

Multiply 2 times 8.

$$-28x^{3}+16x^{2-1}-3x^{1-1}$$

Subtract 1 from 2.

$$-28x^{3}+16x^{1}-3x^{1-1}$$

Subtract 1 from 1.

$$-28x^{3}+16x^{1}-3x^{0}$$

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

$$-28x^{3}+16x-3x^{0}$$

For any term t except 0, t^{0}=1.

$$-28x^{3}+16x-3$$

Evaluate

$$5-3x+8x^{2}-7x^{4}$$