Solve 15x^6-5x^4+25x^3div5x

$$15 x ^ { 6 } - 5 x ^ { 4 } + 25 x ^ { 3 } \div 5 x$$

Evaluate

$$15x^{6}$$

Solution Steps

Divide 25x^{3} by 5 to get 5x^{3}.

$$15x^{6}-5x^{4}+5x^{3}x$$

To multiply powers of the same base, add their exponents. Add 3 and 1 to get 4.

$$15x^{6}-5x^{4}+5x^{4}$$

Combine -5x^{4} and 5x^{4} to get 0.

$$15x^{6}$$

Differentiate w.r.t. x

$$90x^{5}$$

Steps Using Definition of a Derivative

Divide 25x^{3} by 5 to get 5x^{3}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(15x^{6}-5x^{4}+5x^{3}x)$$

To multiply powers of the same base, add their exponents. Add 3 and 1 to get 4.

$$\frac{\mathrm{d}}{\mathrm{d}x}(15x^{6}-5x^{4}+5x^{4})$$

Combine -5x^{4} and 5x^{4} to get 0.

$$\frac{\mathrm{d}}{\mathrm{d}x}(15x^{6})$$

The derivative of ax^{n} is nax^{n-1}.

$$6\times 15x^{6-1}$$

Multiply 6 times 15.

$$90x^{6-1}$$

Subtract 1 from 6.

$$90x^{5}$$