Solve -x(-5^3)(5*5^2)+(3*5)-1

$$- x ( - 5 ^ { 3 } ) ( 5 \cdot 5 ^ { 2 } ) + ( 3 \cdot 5 ) - 1$$

Evaluate

$$15625x+14$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 1 and 2 to get 3.

$$\left(-x\right)\left(-5^{3}\right)\times 5^{3}+3\times 5-1$$

Calculate 5 to the power of 3 and get 125.

$$\left(-x\right)\left(-125\right)\times 5^{3}+3\times 5-1$$

Calculate 5 to the power of 3 and get 125.

$$\left(-x\right)\left(-125\right)\times 125+3\times 5-1$$

Multiply -125 and 125 to get -15625.

$$\left(-x\right)\left(-15625\right)+3\times 5-1$$

Multiply 3 and 5 to get 15.

$$\left(-x\right)\left(-15625\right)+15-1$$

Subtract 1 from 15 to get 14.

$$\left(-x\right)\left(-15625\right)+14$$

Multiply -1 and -15625 to get 15625.

$$15625x+14$$

Differentiate w.r.t. x

$$15625$$

Steps Using Derivative Rule for Sum

To multiply powers of the same base, add their exponents. Add 1 and 2 to get 3.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\left(-x\right)\left(-5^{3}\right)\times 5^{3}+3\times 5-1)$$

Calculate 5 to the power of 3 and get 125.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\left(-x\right)\left(-125\right)\times 5^{3}+3\times 5-1)$$

Calculate 5 to the power of 3 and get 125.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\left(-x\right)\left(-125\right)\times 125+3\times 5-1)$$

Multiply -125 and 125 to get -15625.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\left(-x\right)\left(-15625\right)+3\times 5-1)$$

Multiply 3 and 5 to get 15.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\left(-x\right)\left(-15625\right)+15-1)$$

Subtract 1 from 15 to get 14.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\left(-x\right)\left(-15625\right)+14)$$

Multiply -1 and -15625 to get 15625.

$$\frac{\mathrm{d}}{\mathrm{d}x}(15625x+14)$$

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}.

$$15625x^{1-1}$$

Subtract 1 from 1.

$$15625x^{0}$$

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

$$15625\times 1$$

For any term t, t\times 1=t and 1t=t.

$$15625$$