Question

3) Differentiate with respect to x: a) (x²-3x+5)(2x-7)​

Answer 1

To differentiate the given expression (x²-3x+5)(2x-7) with respect to x, we can apply the product rule of differentiation.

Step-by-step explanation:

To differentiate the given expression (x²-3x+5)(2x-7) with respect to x, we can apply the product rule of differentiation. The product rule states that if we have two functions u(x) and v(x), the derivative of their product is given by (u(x)v'(x) + v(x)u'(x)).

So, applying the product rule to the given expression:

(x²-3x+5)(2x-7)' = (x²-3x+5)'(2x-7) + (x²-3x+5)(2x-7)'

Expanding the multiplication and differentiating each term, we get:

(2x-3)(2x-7) + (x²-3x+5)(2)

Simplifying further, this becomes:

4x² - 14x - 6x + 21 + 2x² - 6x + 10

Combining like terms, we have:

6x² - 26x + 31

Answer 2

6x²-26x+31

Step-by-step explanation:

(x²-3x+5)(2x-7)​

=2x³-7x²-6x²+21x+10x-35

=2x³-13x²+31x-35

Now to differentiate:

dx=6x²-26x+31