Solve 3x^2y+2x+1,5x+24

$$3 x ^ { 2 } y + 2 x + 1,5 x + 24$$

Differentiate w.r.t. x

$$6xy+3,5$$

Steps Using Derivative Rule for Sum

Combine 2x and 1,5x to get 3,5x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(3x^{2}y+3,5x+24)$$

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}.

$$2\times 3yx^{2-1}+3,5x^{1-1}$$

Multiply 2 times 3y.

$$6yx^{2-1}+3,5x^{1-1}$$

Subtract 1 from 2.

$$6yx^{1}+3,5x^{1-1}$$

Subtract 1 from 1.

$$6yx^{1}+3,5x^{0}$$

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

$$6yx+3,5x^{0}$$

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

$$6yx+3,5\times 1$$

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

$$6yx+3,5$$

Evaluate

$$3yx^{2}+\frac{7x}{2}+24$$