Solve 5y^8+10y^7div5y+10

$$5 y ^ { 8 } + 10 y ^ { 7 } \div 5 y + 10$$

Evaluate

$$7y^{8}+10$$

Solution Steps

Divide 10y^{7} by 5 to get 2y^{7}.

$$5y^{8}+2y^{7}y+10$$

To multiply powers of the same base, add their exponents. Add 7 and 1 to get 8.

$$5y^{8}+2y^{8}+10$$

Combine 5y^{8} and 2y^{8} to get 7y^{8}.

$$7y^{8}+10$$

Differentiate w.r.t. y

$$56y^{7}$$

Steps Using Derivative Rule for Sum

Divide 10y^{7} by 5 to get 2y^{7}.

$$\frac{\mathrm{d}}{\mathrm{d}y}(5y^{8}+2y^{7}y+10)$$

To multiply powers of the same base, add their exponents. Add 7 and 1 to get 8.

$$\frac{\mathrm{d}}{\mathrm{d}y}(5y^{8}+2y^{8}+10)$$

Combine 5y^{8} and 2y^{8} to get 7y^{8}.

$$\frac{\mathrm{d}}{\mathrm{d}y}(7y^{8}+10)$$

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}.

$$8\times 7y^{8-1}$$

Multiply 8 times 7.

$$56y^{8-1}$$

Subtract 1 from 8.

$$56y^{7}$$