Solve x^{2}*2x^5-(-x^3)x^4+x^6*(-x)=

$$x ^ { 2 } \cdot 2 x ^ { 5 } - ( - x ^ { 3 } ) x ^ { 4 } + x ^ { 6 } \cdot ( - x ) =$$

Evaluate

$$2x^{7}$$

Solution Steps

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

$$x^{7}\times 2-\left(-x^{3}\right)x^{4}+x^{6}\left(-x\right)$$

To multiply powers of the same base, add their exponents. Add 3 and 4 to get 7.

$$x^{7}\times 2-\left(-x^{7}\right)+x^{6}\left(-1\right)x$$

Multiply -1 and -1 to get 1.

$$x^{7}\times 2+x^{7}+x^{6}\left(-1\right)x$$

Combine x^{7}\times 2 and x^{7} to get 3x^{7}.

$$3x^{7}+x^{6}\left(-1\right)x$$

To multiply powers of the same base, add their exponents. Add 6 and 1 to get 7.

$$3x^{7}+x^{7}\left(-1\right)$$

Combine 3x^{7} and x^{7}\left(-1\right) to get 2x^{7}.

$$2x^{7}$$

Differentiate w.r.t. x

$$14x^{6}$$

Steps Using Definition of a Derivative

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(x^{7}\times 2-\left(-x^{3}\right)x^{4}+x^{6}\left(-x\right))$$

To multiply powers of the same base, add their exponents. Add 3 and 4 to get 7.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x^{7}\times 2-\left(-x^{7}\right)+x^{6}\left(-1\right)x)$$

Multiply -1 and -1 to get 1.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x^{7}\times 2+x^{7}+x^{6}\left(-1\right)x)$$

Combine x^{7}\times 2 and x^{7} to get 3x^{7}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(3x^{7}+x^{6}\left(-1\right)x)$$

To multiply powers of the same base, add their exponents. Add 6 and 1 to get 7.

$$\frac{\mathrm{d}}{\mathrm{d}x}(3x^{7}+x^{7}\left(-1\right))$$

Combine 3x^{7} and x^{7}\left(-1\right) to get 2x^{7}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(2x^{7})$$

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

$$7\times 2x^{7-1}$$

Multiply 7 times 2.

$$14x^{7-1}$$

Subtract 1 from 7.

$$14x^{6}$$