Solve (8+3y)+(7y^3-4-8y)

$$( 8 + 3 y ) + ( 7 y ^ { 3 } - 4 - 8 y )$$

Evaluate

$$7y^{3}-5y+4$$

Solution Steps

Subtract 4 from 8 to get 4.

$$4+3y+7y^{3}-8y$$

Combine 3y and -8y to get -5y.

$$4-5y+7y^{3}$$

Differentiate w.r.t. y

$$21y^{2}-5$$

Steps Using Derivative Rule for Sum

Subtract 4 from 8 to get 4.

$$\frac{\mathrm{d}}{\mathrm{d}y}(4+3y+7y^{3}-8y)$$

Combine 3y and -8y to get -5y.

$$\frac{\mathrm{d}}{\mathrm{d}y}(4-5y+7y^{3})$$

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}.

$$-5y^{1-1}+3\times 7y^{3-1}$$

Subtract 1 from 1.

$$-5y^{0}+3\times 7y^{3-1}$$

Multiply 3 times 7.

$$-5y^{0}+21y^{3-1}$$

Subtract 1 from 3.

$$-5y^{0}+21y^{2}$$

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

$$-5+21y^{2}$$