Solve 4x^2-7x^4+x-15

$$4 x ^ { 2 } - 7 x ^ { 4 } + x - 15$$

Differentiate w.r.t. x

$$1+8x-28x^{3}$$

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}.

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

Multiply 2 times 4.

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

Subtract 1 from 2.

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

Multiply 4 times -7.

$$8x^{1}-28x^{4-1}+x^{1-1}$$

Subtract 1 from 4.

$$8x^{1}-28x^{3}+x^{1-1}$$

Subtract 1 from 1.

$$8x^{1}-28x^{3}+x^{0}$$

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

$$8x-28x^{3}+x^{0}$$

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

$$8x-28x^{3}+1$$

Evaluate

$$-7x^{4}+4x^{2}+x-15$$