Question

if y=x3-4x2+5 then dy/dx is equal to

Answer 1

Answer:

3x²-8x

Step-by-step explanation:

Given that,

y=x³-4x²+5

now, differentiate with respect to 'x' on both sides

dy/dx = d/dx (x³-4x²+5)

⇒dy/dx = 3x² -4(2)x +0             (∵d(xⁿ)/dx = n(x)ⁿ⁻¹ & d(constant)/dx = 0)

⇒dy/dx = 3x²-8x

∴dy/dx = 3x²-8x

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Answer 2

Concept:

A derivative of a function with respect to an independent variable is what is referred to as differentiation. Calculus's concept of differentiation can be used to calculate the function per unit change in the independent variable.

A function of x would be y = f(x). Next, the formula for the rate of change of "y" per unit change in "x" is as follows:

dy / dx

If any point 'x' on the function f(x) experiences an infinitesimal change of 'h,' then the derivative of the function is defined as

lim ₙ₋₀ f(x+h)-f(x)/h

(∵d(xⁿ)/dx = n(x)ⁿ⁻¹ & d(constant)/dx = 0)

Given:

y=x³-4x²+5

Find:

then dy/dx is equal to

Solution:

Given that,

y=x³-4x²+5

now, differentiate with respect to 'x' on both sides

dy/dx = d/dx (x³-4x²+5)

⇒dy/dx = 3x² -4(2)x +0             (∵d(xⁿ)/dx = n(x)ⁿ⁻¹ & d(constant)/dx = 0)

⇒dy/dx = 3x²-8x

∴dy/dx = 3x²-8x

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