Solve 6x^2operatorname{da}7x^3-5x^2-4

$$6 x ^ { 2 } \operatorname { da } 7 x ^ { 3 } - 5 x ^ { 2 } - 4$$

Differentiate w.r.t. x

$$30a_{7}dx^{4}-10x$$

Steps Using Derivative Rule for Sum

To multiply powers of the same base, add their exponents. Add 2 and 3 to get 5.

$$\frac{\mathrm{d}}{\mathrm{d}x}(6x^{5}da_{7}-5x^{2}-4)$$

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}.

$$5\times 6a_{7}dx^{5-1}+2\left(-5\right)x^{2-1}$$

Multiply 5 times 6da_{7}.

$$30a_{7}dx^{5-1}+2\left(-5\right)x^{2-1}$$

Subtract 1 from 5.

$$30a_{7}dx^{4}+2\left(-5\right)x^{2-1}$$

Multiply 2 times -5.

$$30a_{7}dx^{4}-10x^{2-1}$$

Subtract 1 from 2.

$$30a_{7}dx^{4}-10x^{1}$$

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

$$30a_{7}dx^{4}-10x$$

Evaluate

$$6a_{7}dx^{5}-5x^{2}-4$$