Solve 11-x*(-x^2)*x^4

$$11 - x \cdot ( - x ^ { 2 } ) \cdot x ^ { 4 }$$

Evaluate

$$x^{7}+11$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 1 and 4 to get 5.

$$11-x^{5}\left(-x^{2}\right)$$

To multiply powers of the same base, add their exponents. Add 5 and 2 to get 7.

$$11-x^{7}\left(-1\right)$$

Multiply -1 and -1 to get 1.

$$11+x^{7}$$

Differentiate w.r.t. x

$$7x^{6}$$

Steps Using Derivative Rule for Sum

To multiply powers of the same base, add their exponents. Add 1 and 4 to get 5.

$$\frac{\mathrm{d}}{\mathrm{d}x}(11-x^{5}\left(-x^{2}\right))$$

To multiply powers of the same base, add their exponents. Add 5 and 2 to get 7.

$$\frac{\mathrm{d}}{\mathrm{d}x}(11-x^{7}\left(-1\right))$$

Multiply -1 and -1 to get 1.

$$\frac{\mathrm{d}}{\mathrm{d}x}(11+x^{7})$$

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}.

$$7x^{7-1}$$

Subtract 1 from 7.

$$7x^{6}$$