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Derivative of:
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Identical expressions
y= three x^ four -5x^3-7x
y equally 3x to the power of 4 minus 5x cubed minus 7x
y equally three x to the power of four minus 5x cubed minus 7x
y=3x4-5x3-7x
y=3x⁴-5x³-7x
y=3x to the power of 4-5x to the power of 3-7x
Similar expressions
y=3x^4+5x^3-7x
y=3x^4-5x^3+7x

The derivative of the function/ y=3x^4-5x^3-7x

Derivative of y=3x^4-5x^3-7x

The solution

You have entered [src]

   4      3      
3*x  - 5*x  - 7*x

$$3 x^{4} - 5 x^{3} - 7 x$$

d /   4      3      \
--\3*x  - 5*x  - 7*x/
dx

$$\frac{d}{d x} \left(3 x^{4} - 5 x^{3} - 7 x\right)$$

Transform

Detail solution

Differentiate $3 x^{4} - 5 x^{3} - 7 x$ term by term:
1. The derivative of a constant times a function is the constant times the derivative of the function.
  1. Apply the power rule: $x^{4}$ goes to $4 x^{3}$
  So, the result is: $12 x^{3}$
2. The derivative of a constant times a function is the constant times the derivative of the function.
  1. The derivative of a constant times a function is the constant times the derivative of the function.
    1. Apply the power rule: $x^{3}$ goes to $3 x^{2}$
    So, the result is: $15 x^{2}$
  So, the result is: $- 15 x^{2}$
3. The derivative of a constant times a function is the constant times the derivative of the function.
  1. The derivative of a constant times a function is the constant times the derivative of the function.
    1. Apply the power rule: $x$ goes to $1$
    So, the result is: $7$
  So, the result is: $-7$
The result is: $12 x^{3} - 15 x^{2} - 7$

The answer is:

$12 x^{3} - 15 x^{2} - 7$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

         2       3
-7 - 15*x  + 12*x

$$12 x^{3} - 15 x^{2} - 7$$

Simplify

The second derivative [src]

6*x*(-5 + 6*x)

$$6 x \left(6 x - 5\right)$$

Simplify

The third derivative [src]

6*(-5 + 12*x)

$$6 \cdot \left(12 x - 5\right)$$

Simplify

The graph

Derivative of y=3x^4-5x^3-7x